So you basically just exactly described military logistics for shipping diesel fuel with diesel trucks. Congratulations you’re an honorary 2nd lieutenant in charge of a supply platoon now.
that depends on wether we work with "all or none" principles or not. Do 1/3 of bananas still counted as 1 or 0. The video approaches the problem feom purely mathematical standpoint, while in real life you will probabbly left out the last banana
@@OldeCat, well, yes, in my world bringing 533.333 bananas to the finish is better than bringing only 533 If we are talking about the real life, you will also not leave that banana -- because going each time by 1km is not "cost effective" You can take 1000 at 0km, move to 200km and drop 600, then return to 0km and repeat (so there will be 1200 at 200km), then go to the start last time, take the rest and bring to the 200. So you will have 600 + 600 + 800 = 2000 at 200km. Then you will take 1000 and move to 533.333km, drop 333.333, return to 200km, grab the rest, and bring to 533.33km 666.666 more. So you will have 1000 at 533.333km (and you don't need to leave something behind)
Yeah the boundary conditions can be improved. This abandoning strategy is even more pronounced when you use smaller than 1km steps. Technically you can turn around every .001 (limit approaching zero).
Given the info presented at the start - a camel with 3,000 bananas that consumes fuel at a rate of 1 banana per kilometer - the answer is zero bananas. And that's only if the camel only eats bananas while transporting bananas. If the camel's fuel rate is 1 BPK whether loaded or empty then it will stop walking 1 kilometer into the return trip. All-in-all, not a very efficient camel.
@@kylen6430sand you know what’s who are also on the brink of starving because they live in the middle of a desert and don’t know how to survive without imports
The camel eats 1000 bananas up front. Now it is juiced to travel 1000 km, so you bring 1000 bananas with you and leave the last 1000 behind. Why else would it be a camel if you couldn't take advantage of the energy storage of the hump?
You're thinking smart. It's like how a car uses a gallon every like 20-50 miles, you don't add more every couple miles you add it all at the start and then refuel as needed.
Of course, as it took the better part of a year to travel the 1000kms, those bananas are nasty and the camel likely has a serious case of the runs from eating rotten bananas.
@@andrewenderfrost8161first, who says kph. Second, have you seen camels move through the desert? I don't doubt, they can go fast for a minute, but not 1000km...
Indeed. You can even do something silly like load 1000 bananas and walk 200 km (and back) while leaving a trail of 600 bananas (approximately in groups of 3 every km). Imagine that. A trail of 600 bananas on the ground and no worry that a single one will be taken by any animal! Then, you can load 1000 bananas and keep on walking while feeding the camel from bananas on the ground. You'll reach 200 km and still have all 1000 bananas avail to drop off. You can walk back by feeding bananas on the ground, and load the final 1000 and walk back to the depot while feeding remaining bananas on the ground. Ta-da! You now have 2000 bananas at a depot 200 km away.
@@AlainDessureaultno need to leave the trail. Just dump the 600 at the 200 mark and go back after having consumed the other 400 for the round trip. Do it one more time and you have 1200 at the first stop and then half trip more and you will have the 2000 at that stop
@@jayschwartz6131 Leaving a 200 km trail is funnier, and it's kinda cool (and cruel) having the camel twice haul 1000 bananas the entire 200 km without the need to eat from its own cargo
I think this might be slightly different depending on if the camel continuously chews bits of banana as he walks vs if he walks 1 km, stops, eats a whole banana, and then starts walking again. In that case, on those 1km return legs he won't need to carry a banana as he already has a stock of bananas at the end of the km waiting for him.
That wouldn’t change anything, you’re changing it from 1 banana per Km in each direction to bananas per Km forwards and 0 backwards, but the forwards and backwards end up being the same unless forwards is larger, so using that strategy the camel will never have more bananas at any point, it will only ever have less specifically when it moves forwards
@@McP1mpin but the question itself says he must eat a banana every kilometer, indicating that the camel eats after each km, the guy in the vid isnt necessarely right
Assuming the camel continuously consumes a fraction of banana for any traveled distance, then yes, the optimal result is 533 1/3. The strategy is to divide the trip into stages where at the start of each stage you have a multiple of 1000 bananas remain. Here's the steps to deliver maximum bananas with fewest stops: * 1st stage: move 200 km; 3 trips forward and 2 backward, 1000 bananas consumed, 2000 remain, 800 km to go. * 2nd stage: move 333 1/3 km further, 2 trips forward and 1 backward, 1000 bananas consumed, 1000 remain, 466 2/3 km to go. * 3rd stage: move all the way to destination; 466 2/3 bananas consumed, 533 1/3 remain.
The 1k at-a-time works but is nonsense. Unnecessary unloads and reloads. The answer is: Stage 1: Load 1000 b's, eat 200 to go 200 km. Drop 600 b's and eat 200 to walk back. Load 1000 b's, eat 200 to go 200 km. Drop 600 b's and eat 200 to walk back. Load 1000 b's, eat 200 to go 200 km. Drop 800 b's. No walk back. (Drop zone has 600 + 600 + 800 = 2000 b's) Stage 2: Load 1000 b's, eat 333 1/3 to go 333 1/3 km. Drop 333 1/3 b's and eat 333 1/3 to walk back. Load 1000 b's, eat 333 1/3 to go 333 1/3 km. Drop 666 2/3 b's. No walk back. (Drop zone has 333 1/3 + 666 2/3 = 1000 b's) Stage 3: Load 1000 b's, eat 466 1/3 to go 466 1/3 km. Drop 533 1/3 b's. No walk back. We can prove THIS is an optimal strategy
If this was a math test you would have failed because the question was clearly "How many bananas can be transported". It nowhere says all bananas had to reach the destination nor whether it was possible or not to get any banana to the destination
@jayschwartz6131 Less than if I were to drive them there with a truck. Plus where exactly are you leaving these bananas on the ground in the sun without spoiling or some animal stealing them? because it aint gonna 533 by the end, I'll tell ya hwhat. You telling me you precisely stashed these dead drops before hand? Or are you carrying materials along side to build these way stations? Which implies that you could be carrying more bananas. Point is the logic in the question itself doesn't hold when you consider the implications. If you are at this point in your life, your biggest problem isn't the bananas, it's your decision making. Not once did this question even consider how you're getting back home with 533 and 1/3 for this 1000km route, let alone supporting your family/lifestyle with this shit job. Also, can Camel's live off a straight banana diet? Won't it mess with his gut ecosystem at some point? Did you bring water or other sustenance. That Camel is gonna get diabetic by the end. You don't need to be a mathematic genius to figure out that this is not a sustainable business model.
This is NOT a "lower bound". The 533 1/3 bananas delivered is the maximum possible. BUT, the 1-km-at-a-time strategy is unreasonable. It causes unnecessary cargo unloads and reloads. A better idea is to create depots and always move 1000 b's at a time, never less. Moving 3000 bananas takes 5 walks (fwd, bk, fwd, bk, fwd). We want the camel to eat 1000 b's, so it walks 1000 km over 5 walks, therefore 200 km per walk, therefore depot 1 is at 200 km mark and ends up with 2000 bananas. Then, moving 2000 bananas takes 3 walks (fwd, bk, fwd). We want the camel to eat 1000 b's, so it walks 1000 km over 3 walks, therefore 333 1/3 km per walk, therefore depot 2 is at 533 1/3 km mark and ends up with 1000 bananas. Then, moving 1000 bananas takes only one walk (fwd). There's only 466 2/3 km to go. The camel will eat 466 2/3 b's and leave 533 1/3 bananas at the end.
@@shohamsen8986 What @AlainDessureault (and the guy in the video, kinda) did is split the journey into segments: On the first one, the camel transports bananas forward three times, returning twice to do so. On the second one, it transports bananas forward twice, returning once; the third segment is covered only once. Any reasonable strategy can be described by stating where these three segments start and end, including the possibility that a segment might get the same start and end point, which accounts for the idea to leave a segment out entirely. (You could also add segments with more than three forwards trips, which would obviously just be unnecessary extra distance, since there is no point where we have more bananas than the camel could carry in three goes. Anything else that isn't simply an adjustment of how long you choose these three segments to be should rule itself out quite easily, e.g. adding detours for no reason at all.) Now, here's the thing: As the segments are in this solution, the first segment ends and the second one begins exactly at the point where there are 2000 bananas left, based on the rate of bananas per km in the first segment. If it ended any earlier, the next two segments would have to cover a greater distance. There would be more bananas, but segment #2 can't carry more than 2000 bananas away from its starting point, so the excess bananas would be irrelevant. At the end of the day, this would only increase the distance we have to cover powered by 2000 instead of 3000 bananas. If we instead chose to end segment #1 further from the starting point, we would add more distance covered at the unfavourable rate of 5 bananas/km, as opposed to 3 in segment #2. The remaining segments would have less overall distance left to cover, but for each km they save, they get five bananas less, which is more than either of them would have needed to cover that km. Therefore, choosing to end segment #1 at 200km is the option that brings 2000 bananas the furthest. By pretty much the same argument, ending segment #2 at 533.3km gets 1000 bananas the furthest ahead, and at that point, it should be obvious that going straight to the finish line, initially carrying all 1000 bananas, is the most efficient option.
@@shohamsen8986 Other people suggest dropping bananas to reduce the no. Of trips taken, so as to increase the efficiency of the bananas to be used as fuel. However this means that you'd have used up bananas at ZERO EFFICIENCY by dropping them, so it's actually better to not drop any bananas, and take any non-zero efficiency you can get. The trips at the start and end of the first phase have efficiency of 600m and 400m per banana respectively, averaging 500. This is certainly less than 666.67m per banana efficiency at the start of second phase, but dropping 1000 or 1 banana would still decrease this efficiency. Even if you have an odd banana e.g. having 2001 bananas, better to carry all the bananas by 5 trips for a distance of 200m, then start doing 3 trips. If you dropped that odd banana you'd lose 4/5 of a banana (3/5 in 2nd phase and 1/5 in 3rd phase). So for this reason all of your phases should start with zero dropped bananas i.e. you should be dragging the earliest phases for the longest before starting a new one, so that newer phases do start with 0 drops. Also, the camel cannot move to the 3-trip region while having dropped bananas in 5-trip region, as the return trip would be more inefficient, hence the solution would not be ideal. So the bananas always need to be dropped at the end of the current region or at the start of the next region, before transitioning.
@@enderofbarts exactly. and if this is technically most optimal, I'd say it is still a good idea, because if we're not gonna question a camel eating majority of the 3000 bananas it is trying to transport then we shouldn't question a camel eating a a Planck length piece of banana.
You've fallen victim to one of the classic blunders! Never underestimate the ingenuity of a camel when bananas are on the line. What's the camel's reach? If he can load and unload all these bananas without any cost, there's no reason he couldn't transport unlimited bananas. He just has to move a little bit at a time and reach back to pick up the whole pile before dropping it at his feet. After eating his cut he'd move 2000 bananas the full kilometer!
Advanced math is determining exactly how many bananas you will be able to save, economics is using that data to understand that any business that consumes more resources than it sells is a bad idea for a business. Invest early in an efficient non-banana-consuming transportation with a business loan.
- Camel carries 1000 bananas on first trip - Goes to the 250th kilometer, has 750 bananas left - Leaves 500 bananas, returns to initial point. - Repeats the process once, the 250th kilometer has 1000 bananas now - Takes the remaining 1000 bananas from the initial point and goes to the 250th kilometer. Now the camel has 750 bananas and, with the bananas it already left, 1750 bananas in total. - Takes 1000 bananas from the 250th km, and goes to the 500th km. It has 750 bananas left. Leaves 500 and returns - Takes the remaining 750 bananas from the 250th km, and returns to the 500th km. It has 500 bananas left, 1000 bananas in total. - Goes to the 1000th km. Has 500 bananas left This one has 33⅓ bananas less, but also much fewer backs and forths, only 9 in total.
@@daniel_wiersma It requires more bananas because the camel eats 1 banana per km, no matter how many bananas is carrying. So, in order to be more efficient, you need the camel to be at full capacity most of the time. I bet you will get a slightly better result with half km steps. There must be a case with infinite steps of negligible length for the upper limit.
@@fca003this solution is lacking in the optimization that occurs when you first drop to 2000 bananas. I believe that as long as your increment of distance hits the optimization at 2000 and 1000 bananas you will hit 533.33 and cannot be improved by going smaller in increment
Theres so many implications this "riddle" has. If someone asks you this, it isn't a riddle. This isn't even a 5th grade question. This is a cry for help. What decisions did they make that led them to commiting to such a dubious business model?
D'oh! You're right. I thought it was impossible because you would no longer have all the 3000 bananas that have to be transported once the camel has consumed any of the bananas, but I made the assumption that it had to be the camel that was the method of transportation.
Depends what you mean by "the solution" The 533 1/3 bananas delivered is indeed the maximum possible. BUT, the 1-km-at-a-time strategy is unreasonable. It causes unnecessary cargo unloads and reloads. A better idea is to create depots and always move 1000 b's at a time, never less. This eliminates unnecessary consumption of bananas. Moving 3000 bananas takes 5 walks (fwd, bk, fwd, bk, fwd). We want the camel to eat 1000 b's, so it walks 1000 km over 5 walks, therefore 200 km per walk, therefore depot 1 is at 200 km mark and ends up with 2000 bananas. Then, moving 2000 bananas takes 3 walks (fwd, bk, fwd). We want the camel to eat 1000 b's, so it walks 1000 km over 3 walks, therefore 333 1/3 km per walk, therefore depot 2 is at 533 1/3 km mark and ends up with 1000 bananas. Then, moving 1000 bananas takes only one walk (fwd). There's only 466 2/3 km to go. The camel will eat 466 2/3 b's and leave 533 1/3 bananas at the end.
The answer is 533, no decimal. The problem does not specify that the camel runs on fractions of bananas, and only whole integers have been given. We cannot logically assume from the givens that the camel consumes 1/3 banana to travel 1/3 km. If the camel has just eaten, and it travels 1/3 km, it may not be hungry again to consume any more banana. (Also, if the camel is hungry, we dont know if it will move again without consuming a full banana) It makes no sense to assume from whats given. So we would go 467m starting with 1000 and ending with 533.
also, allowing fractional bananas could give solutions that would get very close to transporting all 3000 bananas as the camel walks smaller and smaller distances. the limit approaches 3000
Gotta love riddles relying on you to decide what is allowable outside of the parameters of the puzzle. Dropping bananas? AOK. Calling in an airplane to do it for you? Probably not in the spirit of the riddle for some reason.
You forgot that you have left bananas unattended on the side of the road. When you arrive to the banana pile after your 42nd 2 km round trip, you find monkeys have eaten half, and thieves have taken the other half.
How many meters are We assuming the camel moves each time he does? Surely it cannot be one kilometer while carrying 1000 bananas as that would make him not move (or go backwards 9000 meters 😂😂).
How long does the camel take? Bananas have a specific shelf life, and I assume the bananas are being transported through heat, its going to only be one trip before any leftover bananas are no longer consumable.
a camel can go for about 50km/day - that is under the hypothesis that our camel has the muscle strength of any other camel and the fact that he can only carry 1000 bananas at a time (around 180kg against the normal 450 ones) is due to the fact that it is also carrying other things (probably one person, boxes to put the bananas in, and possibly a palanquin of some sort. please understand that this is quite unprofessional - the person should walk and let the camel transport 2000 bananas per trip instead) that said 1000 km : 50 km/day is 20 days. which is way more than the shelf life of a banana. unless the reduced weight the camel is able to transport is due to some kind of contraption (like a battery-powered freezer of some sort) thought to increase the bananas' shelf life edit: alas I have been unable to find out how much a camel is supposed to eat in a day, especially of it's bananas which are not its primary diet. but since a camel can actually not eat for 15 days I will take the hypothesis that even if we are not overfeeding it (50 bananas a day do seem a bit of overfeeding for a camel - maybe it is weaker than normal because it's fat?) we could most certainly reduce the amount. just let it eat before the trip and at the end and you will probably only need to feed it abundantly once midway.
Wow I already thought that my idea of going step by step by one kilometer is wrong. Well in russia we call it "the quieter you go - the further you go"
@@AbsoluteHuman The original joke was about people buying watermelons for 50 cents each, and then selling them for two for a dollar, and not understanding why they weren't making any profit. They consulted with a friend, who told them "Fools, don't you know you need a bigger truck?"
*Unexpected event has happened* The camel was too exhausted for continuing the trip, it died after the 400s km. Now you're alone with 2600 bananas and a task. Now you may carry at max 100 bananas every trip and have to eat 1 every km, they must arrive at a 600km distance
If given our current technology, I think the answer is still 0 because the bananas would probably have all rotted before the camel would be able to do all that.
The explanation is interesting, but now I am wondering how you figured out you had to go back an forth 1km until 200km? What calculations did you make in order to determine it was optimal at 200km?
Don't think in terms of km but in terms of bananas. When you have 2000-3000, you need 3 trips per km because the camel can carry up to 1000 bananas. When you have 1000-2000, you need 2 trips per km, and when you have 1000 bananas, you just need a single trip. The 200 km mark is the point when you go below 2000 bananas since you sacrifice 5 bananas per km (1000bananas ÷ 5 bananas = 200 trips of 1km = 200km). Same logic from there on.
We're assuming it's monotone and the optimum must be at one or other extreme. There wasn't any argumentation showing that there was no better solution. For example, take 1000 bananas 200km dropping 600 and returning for the next 1000. My intuition says that most cases where you don't run out of bananas are equivalent, but if have to do it long hand to convince myself
@@stevecarter8810someone mentioned shorter increments such as .0001 km but I tried doing .5 km increments and it turned out the same as 1 km so my guess is as long as you always start trips with 1000 or whatever is left it will be 533.33333 or you won't make it.
I first rephrased the problem: since the camel can go back and forth, it can transport 2000 bananas when eating 3 bananas per km and 3000 bananas when eating 5 bananas per km. So let it start with 3000 bananas, after 200 km 2000 are left. After another 333⅓ km 1000 are left (note the camel actually walked 1000 km in each of the first two phases, but the bananas only made 200 km and 333⅓ km progress). Now with these 1000 left it can walk the remaining 466⅔ km, which consumes another 467 (rounded up) and leaving you with 533 bananas. The camel walked 2466⅔ km to transport them. EDIT: Note that the camel doesn't have to stop every km. Simplified tour: Load 1000 at km 0 (0→1000) Unload 600 at km 200 (800→200) Load 1000 at km 0 (0→1000) Unload 600 at km 200 (800→200) Load 1000 at km 0 (0→1000) Load 200 at km 200 (800→1000) Unload 333 at km 533⅓ (666*→333) Load 1000* at km 200 (0*→1000) Load 333 at km 533⅓ (667*→1000) Unload 533 at km 1000 (533*→0) *(assuming it eats bananas before walking the 1km rather than after)
Theoretically wouldn’t that mean if you did the little return trip method with less than 1km it would be more and more efficient the less each trip was?
Time stamping this now 0:19 havent seen the answer yet, 1000 bananas, bring him halfway, you’ve lost 500 bananas, bring him back, now hes carrying no bananas since he ate them all, add another 1000, bring him 250km, you have 750 left, bring him back, you have 500 left, put another 500 leaving 1000 behind, call your friend with another camel and have him bring you the rest. But wait. Zero bananas left. Oh well
The question is "How many bananas can be transported 1,000km?" It's a trick question, it doesn't say they have to be done all at once or how many are left by the end of the trip. The only rigid rule there is the distance and the material good. However many bananas one has access to, theoretically an infinite amount of bananas, can be transported across 1,000km.
You know what..... you're right. It should have said: "Given the context provided, how many bananas can be transported in 1000km?" In this case, this is the same meme as "Find X" and circling X in the problem.
The real solution is different, but delivers the same 533 1/3 bananas. (By real solution, I mean the most reasonable) You move in 5 walks the 3000 to 200 km mark - creating a 2000 banana depot. You move in 3 walks the 2000 to the 533 1/3 km mark - creating a 1000 banana depot. You move in 1 walk the 1000 to the end - delivering 533 1/3 bananas.
I just woke up and solved this riddle in my head. Thanks for the mourning exercise. Although, as some commenters pointed out, it is more effective to abandon 1 banana at 1001. Also I don't think that you can eat fractions of bananas because in that case the smaller parts of banana you eat per turn, the more effectively you transport them... hmmm. This could make a nice calculus problem.
Depends on what you mean by solution. The 533 1/3 bananas at the end IS the maximum amount, but the 1 km at-a-time strategy is nonsense. It causes unnecessary unloads and reloads of cargo. The most reasonable way is as follows: Stage 1: Load 1000 b's, eat 200 to go 200 km. Drop 600 b's and eat 200 to walk back. Load 1000 b's, eat 200 to go 200 km. Drop 600 b's and eat 200 to walk back. Load 1000 b's, eat 200 to go 200 km. Drop 800 b's. No walk back. (Drop zone has 600 + 600 + 800 = 2000 b's) Stage 2: Load 1000 b's, eat 333 1/3 to go 333 1/3 km. Drop 333 1/3 b's and eat 333 1/3 to walk back. Load 1000 b's, eat 333 1/3 to go 333 1/3 km. Drop 666 2/3 b's. No walk back. (Drop zone has 333 1/3 + 666 2/3 = 1000 b's) Stage 3: Load 1000 b's, eat 466 1/3 to go 466 1/3 km. Final drop 533 1/3 b's. No walk back. An argument can be made from this strategy to show that no better delivery is possible.
I hoped there would be a mathematical proof that this is the most optimal solution. Just because the total opposite is worse doesn't necessarily mean this is the optimum.
Want to take this a step further! Now distinguish the mathematical equation out of this so we can calculate it faster without going in this whole story
This is the perfect analogy for how the government spends our tax money. The government (camel) says go stand over there while we create something valuable with your tax dollars (bananas). Except they use the first strategy then demand more bananas when they show up, having eaten all their bananas on the journey with nothing left to show for it.
The solution with the least trips would be to have the camel deliver 200 bananas to 400km twice then pick them up in the last trip which would make it 5 trips total with 400 bananas left over.
I'd go 1000km with the camel with 1000 bananas, sell that camel to rent a car, and go get the rest of the 2000 bananas. Keeping that camel is a liability.
The ability to arbitrarily deposit bananas definitely needed to be part of the problem statement. People often won't come up with something unprompted if it is nonsensical in reality. Abandoning your cargo on the road is a good way to have it be stolen or damaged by the elements. A reasonable person wouldn't take that liberty. So it's not something you can expect people to infer as part of a puzzle.
What if the camel eats 1000 bananas at starting & carry 1000 banana on him, that would gave him the energy to travel 1000 km with 1000 banana on his back. By this maximum number of bananas that can be transported is 1000.
Surely the answer is: it's impossible. The second line says 'the bananas' which refers to the 3000 bananas on the first line. However you load the camel, once it has moved any distance you will have fewer than 3000 bananas because at least a proportion of a banana has been eaten. Therefore the 3000 bananas can't be transported 1000 km.
This information is imperative for my banana camel transportation business I am planning on starting. Thank you!
Just as long as you don't get in the way of my mango camel transportation business.
It sounds very inefficient though.
I hope you're reporting your earnings to the irs
"Dont interupt my monkey buisness."
I tell you what, I transport my bananas by elephant because they work for peanuts.
"Has the tanker arrived with 3000 gallons of petrol?"
"Uh, you mean 500 gallons?"
Who's drinking the petrol bro
@@GoKeWhOthe tanker
@@GoKeWhOme
@@Thot-Slayer-420 found the dinker
"You don't need 3000 gallons of petrol, when you got family"
-Dominic Toretto
So you basically just exactly described military logistics for shipping diesel fuel with diesel trucks. Congratulations you’re an honorary 2nd lieutenant in charge of a supply platoon now.
Except I don’t think you can just drop off fuel on the path go back, and pick up the fuel you left.
just realized, at 1001 it's more cost effective to just abandon the last one banana
Nope, if you abandon banana, you start full at 533
If you go back for the 1001-st, you can start full at 533.333
that depends on wether we work with "all or none" principles or not. Do 1/3 of bananas still counted as 1 or 0. The video approaches the problem feom purely mathematical standpoint, while in real life you will probabbly left out the last banana
@@OldeCat, well, yes, in my world bringing 533.333 bananas to the finish is better than bringing only 533
If we are talking about the real life, you will also not leave that banana -- because going each time by 1km is not "cost effective"
You can take 1000 at 0km, move to 200km and drop 600, then return to 0km and repeat (so there will be 1200 at 200km), then go to the start last time, take the rest and bring to the 200.
So you will have 600 + 600 + 800 = 2000 at 200km. Then you will take 1000 and move to 533.333km, drop 333.333, return to 200km, grab the rest, and bring to 533.33km 666.666 more.
So you will have 1000 at 533.333km (and you don't need to leave something behind)
Yeah the boundary conditions can be improved. This abandoning strategy is even more pronounced when you use smaller than 1km steps. Technically you can turn around every .001 (limit approaching zero).
Given the info presented at the start - a camel with 3,000 bananas that consumes fuel at a rate of 1 banana per kilometer - the answer is zero bananas. And that's only if the camel only eats bananas while transporting bananas. If the camel's fuel rate is 1 BPK whether loaded or empty then it will stop walking 1 kilometer into the return trip. All-in-all, not a very efficient camel.
I think the optimal strategy is to sell 2000 bananas where you are, bring 1000 bananas 1000km, then sell the camel at that destination.
Who’s gonna buy an exhausted camel on the brink of starvation?!
@@kylen6430sand you know what’s who are also on the brink of starving because they live in the middle of a desert and don’t know how to survive without imports
@@kylen6430 it's not on the brink of starvation it just ate a thousand bananas!!!
Sell the camel and a thousand banana to buy an E-cycle and some extra batteries.
@@simontmillerfalse, it ate 2,467 bananas. 😄
If I'm ever in a situation like this, I've made a series of horrendous life choices.
This is the life of people who work in logistics lol
The camel eats 1000 bananas up front. Now it is juiced to travel 1000 km, so you bring 1000 bananas with you and leave the last 1000 behind. Why else would it be a camel if you couldn't take advantage of the energy storage of the hump?
Agree
If you can juice up before hand just have it ready 2000 and it will be worth more when you sell the still juices up camel.
Or feed it 2000 so u get ur camel back home
You're thinking smart. It's like how a car uses a gallon every like 20-50 miles, you don't add more every couple miles you add it all at the start and then refuel as needed.
Of course, as it took the better part of a year to travel the 1000kms, those bananas are nasty and the camel likely has a serious case of the runs from eating rotten bananas.
Actually you can do it in a couple of months, but the point stands. Bananas go bad fast.
They weren't organic
At 65 kph, and 2467 km it took them 37.95 hours not including dropping off the load and eating. This would take less than a week
@@andrewenderfrost8161first, who says kph. Second, have you seen camels move through the desert? I don't doubt, they can go fast for a minute, but not 1000km...
@@andrewenderfrost8161that is one fast camel. Camel walking speed is 5kph and max running speed is 25kph.
This became a whole lot easier when I heard we're allowed to just dump the bananas anywhere without worrying something will happen to them. 😂
Indeed.
You can even do something silly like load 1000 bananas and walk 200 km (and back) while leaving a trail of 600 bananas (approximately in groups of 3 every km).
Imagine that. A trail of 600 bananas on the ground and no worry that a single one will be taken by any animal!
Then, you can load 1000 bananas and keep on walking while feeding the camel from bananas on the ground.
You'll reach 200 km and still have all 1000 bananas avail to drop off.
You can walk back by feeding bananas on the ground, and load the final 1000 and walk back to the depot while feeding remaining bananas on the ground.
Ta-da! You now have 2000 bananas at a depot 200 km away.
@@AlainDessureaultno need to leave the trail. Just dump the 600 at the 200 mark and go back after having consumed the other 400 for the round trip. Do it one more time and you have 1200 at the first stop and then half trip more and you will have the 2000 at that stop
@@jayschwartz6131
Leaving a 200 km trail is funnier, and it's kinda cool (and cruel) having the camel twice haul 1000 bananas the entire 200 km without the need to eat from its own cargo
The first time I saw this riddle, I just gave up... I never considered the idea that you could drop bananas off without being near them, lol
I thought this was a math question tbh
My thought process was someone or something could take them. That or they would spoil in the sun.
I think this might be slightly different depending on if the camel continuously chews bits of banana as he walks vs if he walks 1 km, stops, eats a whole banana, and then starts walking again. In that case, on those 1km return legs he won't need to carry a banana as he already has a stock of bananas at the end of the km waiting for him.
Similarly, what if the camel must eat a banana before walking a kilometer?
Well he ate a third of a banana which means he must be eating as he goes.
What if the camel gets tired of eating bananas and gives up?
That wouldn’t change anything, you’re changing it from 1 banana per Km in each direction to bananas per Km forwards and 0 backwards, but the forwards and backwards end up being the same unless forwards is larger, so using that strategy the camel will never have more bananas at any point, it will only ever have less specifically when it moves forwards
@@McP1mpin but the question itself says he must eat a banana every kilometer, indicating that the camel eats after each km, the guy in the vid isnt necessarely right
I saw this on your Instagram story and suddenly felt the need to know how many bananas it takes. How exciting indeed!!
But if he has 2001 bananas left, it's not worth the return trip for that last banana
He wouldn't end up with 2001 because the first 200km consume 5 bananas per km.
That's not what Jesus taught us
You mean at 1001 Bananas*
I feel like this isnt a riddle. Its a math problem in disguise
Assuming the camel continuously consumes a fraction of banana for any traveled distance, then yes, the optimal result is 533 1/3. The strategy is to divide the trip into stages where at the start of each stage you have a multiple of 1000 bananas remain.
Here's the steps to deliver maximum bananas with fewest stops:
* 1st stage: move 200 km; 3 trips forward and 2 backward, 1000 bananas consumed, 2000 remain, 800 km to go.
* 2nd stage: move 333 1/3 km further, 2 trips forward and 1 backward, 1000 bananas consumed, 1000 remain, 466 2/3 km to go.
* 3rd stage: move all the way to destination; 466 2/3 bananas consumed, 533 1/3 remain.
This question has been troubling me for years. Thanks for clearing it up.
You need to learn this in case a mugger asked you to solve this problem in exchange for not taking your money.
He worked so hard, just give him the 1/3 banana as well 😫
Can you prove this is the optimal strategy?
Exactly. You need to show that here is upper limit of what the camel can deliver.
Yeah, he demonstrates this strategy but we don't know whether there's another one that's more efficient :/
Yeah, the 1km step seems arbitrary, and as other comments have pointed out sometimes abandoning bananas might be more efficient
I'm fairly certain the smaller distance traveled per trip would also result in higher yield but I'd like to see this actually written out fully
The 1k at-a-time works but is nonsense. Unnecessary unloads and reloads.
The answer is:
Stage 1:
Load 1000 b's, eat 200 to go 200 km. Drop 600 b's and eat 200 to walk back.
Load 1000 b's, eat 200 to go 200 km. Drop 600 b's and eat 200 to walk back.
Load 1000 b's, eat 200 to go 200 km. Drop 800 b's. No walk back.
(Drop zone has 600 + 600 + 800 = 2000 b's)
Stage 2:
Load 1000 b's, eat 333 1/3 to go 333 1/3 km. Drop 333 1/3 b's and eat 333 1/3 to walk back.
Load 1000 b's, eat 333 1/3 to go 333 1/3 km. Drop 666 2/3 b's. No walk back.
(Drop zone has 333 1/3 + 666 2/3 = 1000 b's)
Stage 3:
Load 1000 b's, eat 466 1/3 to go 466 1/3 km. Drop 533 1/3 b's. No walk back.
We can prove THIS is an optimal strategy
This problem had so much appeal.
It's bananas, isn't it?
It was ripe for discussion.
Thanks a bunch for these puns, fellas.
Im surprised he didn't slip up more
Except that you needed to deliver 3000 bananas, so you are short 2400+ bananas... mission failure
lol
If this was a math test you would have failed because the question was clearly "How many bananas can be transported". It nowhere says all bananas had to reach the destination nor whether it was possible or not to get any banana to the destination
@jayschwartz6131 Less than if I were to drive them there with a truck. Plus where exactly are you leaving these bananas on the ground in the sun without spoiling or some animal stealing them? because it aint gonna 533 by the end, I'll tell ya hwhat. You telling me you precisely stashed these dead drops before hand? Or are you carrying materials along side to build these way stations? Which implies that you could be carrying more bananas.
Point is the logic in the question itself doesn't hold when you consider the implications. If you are at this point in your life, your biggest problem isn't the bananas, it's your decision making.
Not once did this question even consider how you're getting back home with 533 and 1/3 for this 1000km route, let alone supporting your family/lifestyle with this shit job.
Also, can Camel's live off a straight banana diet? Won't it mess with his gut ecosystem at some point? Did you bring water or other sustenance. That Camel is gonna get diabetic by the end.
You don't need to be a mathematic genius to figure out that this is not a sustainable business model.
@@RustedBuddy5192It's a mathematical riddle, of course it doesn't have real-life applications
This is rocket science in a nutshell.
If Tsiolkovsky were born in Africa.
This is a lower bound. What is your argument for this being optimal?
This is NOT a "lower bound". The 533 1/3 bananas delivered is the maximum possible.
BUT, the 1-km-at-a-time strategy is unreasonable. It causes unnecessary cargo unloads and reloads.
A better idea is to create depots and always move 1000 b's at a time, never less.
Moving 3000 bananas takes 5 walks (fwd, bk, fwd, bk, fwd). We want the camel to eat 1000 b's, so it walks 1000 km over 5 walks, therefore 200 km per walk, therefore depot 1 is at 200 km mark and ends up with 2000 bananas.
Then, moving 2000 bananas takes 3 walks (fwd, bk, fwd). We want the camel to eat 1000 b's, so it walks 1000 km over 3 walks, therefore 333 1/3 km per walk, therefore depot 2 is at 533 1/3 km mark and ends up with 1000 bananas.
Then, moving 1000 bananas takes only one walk (fwd). There's only 466 2/3 km to go. The camel will eat 466 2/3 b's and leave 533 1/3 bananas at the end.
@@AlainDessureault how do u know its optimal?
@@shohamsen8986 What @AlainDessureault (and the guy in the video, kinda) did is split the journey into segments: On the first one, the camel transports bananas forward three times, returning twice to do so. On the second one, it transports bananas forward twice, returning once; the third segment is covered only once. Any reasonable strategy can be described by stating where these three segments start and end, including the possibility that a segment might get the same start and end point, which accounts for the idea to leave a segment out entirely. (You could also add segments with more than three forwards trips, which would obviously just be unnecessary extra distance, since there is no point where we have more bananas than the camel could carry in three goes. Anything else that isn't simply an adjustment of how long you choose these three segments to be should rule itself out quite easily, e.g. adding detours for no reason at all.) Now, here's the thing: As the segments are in this solution, the first segment ends and the second one begins exactly at the point where there are 2000 bananas left, based on the rate of bananas per km in the first segment. If it ended any earlier, the next two segments would have to cover a greater distance. There would be more bananas, but segment #2 can't carry more than 2000 bananas away from its starting point, so the excess bananas would be irrelevant. At the end of the day, this would only increase the distance we have to cover powered by 2000 instead of 3000 bananas. If we instead chose to end segment #1 further from the starting point, we would add more distance covered at the unfavourable rate of 5 bananas/km, as opposed to 3 in segment #2. The remaining segments would have less overall distance left to cover, but for each km they save, they get five bananas less, which is more than either of them would have needed to cover that km. Therefore, choosing to end segment #1 at 200km is the option that brings 2000 bananas the furthest. By pretty much the same argument, ending segment #2 at 533.3km gets 1000 bananas the furthest ahead, and at that point, it should be obvious that going straight to the finish line, initially carrying all 1000 bananas, is the most efficient option.
Well, you can find out for yourself. If you are too lazy to do it, close your eyes and take it in from your behind
@@shohamsen8986
Other people suggest dropping bananas to reduce the no. Of trips taken, so as to increase the efficiency of the bananas to be used as fuel. However this means that you'd have used up bananas at ZERO EFFICIENCY by dropping them, so it's actually better to not drop any bananas, and take any non-zero efficiency you can get. The trips at the start and end of the first phase have efficiency of 600m and 400m per banana respectively, averaging 500. This is certainly less than 666.67m per banana efficiency at the start of second phase, but dropping 1000 or 1 banana would still decrease this efficiency.
Even if you have an odd banana e.g. having 2001 bananas, better to carry all the bananas by 5 trips for a distance of 200m, then start doing 3 trips. If you dropped that odd banana you'd lose 4/5 of a banana (3/5 in 2nd phase and 1/5 in 3rd phase).
So for this reason all of your phases should start with zero dropped bananas i.e. you should be dragging the earliest phases for the longest before starting a new one, so that newer phases do start with 0 drops.
Also, the camel cannot move to the 3-trip region while having dropped bananas in 5-trip region, as the return trip would be more inefficient, hence the solution would not be ideal. So the bananas always need to be dropped at the end of the current region or at the start of the next region, before transitioning.
Trick question. The bananas will spoil long before the camel makes it to the destination.
If you allow for fractional banana consumption wouldn’t the optimal strat be to make as small trips as possible?
So the camel eats the Planck length off a banana…
...to travel an infinitessimally small distance
@@enderofbarts exactly. and if this is technically most optimal, I'd say it is still a good idea, because if we're not gonna question a camel eating majority of the 3000 bananas it is trying to transport then we shouldn't question a camel eating a a Planck length piece of banana.
You've fallen victim to one of the classic blunders!
Never underestimate the ingenuity of a camel when bananas are on the line.
What's the camel's reach? If he can load and unload all these bananas without any cost, there's no reason he couldn't transport unlimited bananas. He just has to move a little bit at a time and reach back to pick up the whole pile before dropping it at his feet.
After eating his cut he'd move 2000 bananas the full kilometer!
This is like being overemcumbered in a game but refusing to leave anything
Advanced math is determining exactly how many bananas you will be able to save, economics is using that data to understand that any business that consumes more resources than it sells is a bad idea for a business. Invest early in an efficient non-banana-consuming transportation with a business loan.
- Camel carries 1000 bananas on first trip
- Goes to the 250th kilometer, has 750 bananas left
- Leaves 500 bananas, returns to initial point.
- Repeats the process once, the 250th kilometer has 1000 bananas now
- Takes the remaining 1000 bananas from the initial point and goes to the 250th kilometer. Now the camel has 750 bananas and, with the bananas it already left, 1750 bananas in total.
- Takes 1000 bananas from the 250th km, and goes to the 500th km. It has 750 bananas left. Leaves 500 and returns
- Takes the remaining 750 bananas from the 250th km, and returns to the 500th km. It has 500 bananas left, 1000 bananas in total.
- Goes to the 1000th km. Has 500 bananas left
This one has 33⅓ bananas less, but also much fewer backs and forths, only 9 in total.
I had the same result. Don't understand why this requires more bananas though...
@@daniel_wiersma It requires more bananas because the camel eats 1 banana per km, no matter how many bananas is carrying. So, in order to be more efficient, you need the camel to be at full capacity most of the time.
I bet you will get a slightly better result with half km steps. There must be a case with infinite steps of negligible length for the upper limit.
Nope, I just check it. The result is the same with half km steps ¯\_( •_•)_/¯
@@fca003this solution is lacking in the optimization that occurs when you first drop to 2000 bananas. I believe that as long as your increment of distance hits the optimization at 2000 and 1000 bananas you will hit 533.33 and cannot be improved by going smaller in increment
@@fca003I agree
This guy seems to struggle more and more with the "how interesting" everytime I see him
Theres so many implications this "riddle" has.
If someone asks you this, it isn't a riddle. This isn't even a 5th grade question. This is a cry for help.
What decisions did they make that led them to commiting to such a dubious business model?
3000 bananas, the riddle never says you have to use the camel.
D'oh! You're right. I thought it was impossible because you would no longer have all the 3000 bananas that have to be transported once the camel has consumed any of the bananas, but I made the assumption that it had to be the camel that was the method of transportation.
Do you have any proof that the solution is an optimal one.
Depends what you mean by "the solution"
The 533 1/3 bananas delivered is indeed the maximum possible.
BUT, the 1-km-at-a-time strategy is unreasonable. It causes unnecessary cargo unloads and reloads.
A better idea is to create depots and always move 1000 b's at a time, never less. This eliminates unnecessary consumption of bananas.
Moving 3000 bananas takes 5 walks (fwd, bk, fwd, bk, fwd). We want the camel to eat 1000 b's, so it walks 1000 km over 5 walks, therefore 200 km per walk, therefore depot 1 is at 200 km mark and ends up with 2000 bananas.
Then, moving 2000 bananas takes 3 walks (fwd, bk, fwd). We want the camel to eat 1000 b's, so it walks 1000 km over 3 walks, therefore 333 1/3 km per walk, therefore depot 2 is at 533 1/3 km mark and ends up with 1000 bananas.
Then, moving 1000 bananas takes only one walk (fwd). There's only 466 2/3 km to go. The camel will eat 466 2/3 b's and leave 533 1/3 bananas at the end.
The answer is 533, no decimal. The problem does not specify that the camel runs on fractions of bananas, and only whole integers have been given. We cannot logically assume from the givens that the camel consumes 1/3 banana to travel 1/3 km. If the camel has just eaten, and it travels 1/3 km, it may not be hungry again to consume any more banana. (Also, if the camel is hungry, we dont know if it will move again without consuming a full banana) It makes no sense to assume from whats given. So we would go 467m starting with 1000 and ending with 533.
also, allowing fractional bananas could give solutions that would get very close to transporting all 3000 bananas as the camel walks smaller and smaller distances. the limit approaches 3000
@@sylviaxx3574 No, it absolutely does not.
Gotta love riddles relying on you to decide what is allowable outside of the parameters of the puzzle. Dropping bananas? AOK. Calling in an airplane to do it for you? Probably not in the spirit of the riddle for some reason.
You could leave me in the forest for 100 years and I’d never be able to figure that out.
This is the most inefficient banana transport I have ever seen my cammel can do this with half a banana and carry every other banana.
Pretty sure the real answer is just sell the camel and buy a car it's not the 1200's anymore.
Plot twist: 533 bananas were spoiled on arrival
I guess I'll remember this method if this ever comes up as an obnoxious interview question.
At 1001 bananas...going back for that single banana would actually cost him two more bananas.
You forgot that you have left bananas unattended on the side of the road.
When you arrive to the banana pile after your 42nd 2 km round trip, you find monkeys have eaten half, and thieves have taken the other half.
Now what if the energy expenditure of carrying bananas causes him to travel 10 meters less per banana?
How many meters are We assuming the camel moves each time he does?
Surely it cannot be one kilometer while carrying 1000 bananas as that would make him not move (or go backwards 9000 meters 😂😂).
@@jonnemopola7245i think you just discovered free energy
@@jonnemopola7245 The real strat, make the camel try to move backwards with full load.
@@WhyName But of course! What a masterful plan!
what if the camel is diabetic?
There's ALWAYS money in the banana stand.
And all the bananas have ripened and gone bad by the time the camel got them to the remaining bananas to the destination.
How long does the camel take? Bananas have a specific shelf life, and I assume the bananas are being transported through heat, its going to only be one trip before any leftover bananas are no longer consumable.
a camel can go for about 50km/day - that is under the hypothesis that our camel has the muscle strength of any other camel and the fact that he can only carry 1000 bananas at a time (around 180kg against the normal 450 ones) is due to the fact that it is also carrying other things (probably one person, boxes to put the bananas in, and possibly a palanquin of some sort. please understand that this is quite unprofessional - the person should walk and let the camel transport 2000 bananas per trip instead)
that said 1000 km : 50 km/day is 20 days.
which is way more than the shelf life of a banana.
unless the reduced weight the camel is able to transport is due to some kind of contraption (like a battery-powered freezer of some sort) thought to increase the bananas' shelf life
edit: alas I have been unable to find out how much a camel is supposed to eat in a day, especially of it's bananas which are not its primary diet. but since a camel can actually not eat for 15 days I will take the hypothesis that even if we are not overfeeding it (50 bananas a day do seem a bit of overfeeding for a camel - maybe it is weaker than normal because it's fat?) we could most certainly reduce the amount. just let it eat before the trip and at the end and you will probably only need to feed it abundantly once midway.
Leaving the banana cargo out in the sand as you double back for more bananas doesn't seem like a good idea either
This riddle is about math not camels biology
@@RotatingLocomotive spoilsport
@@RotatingLocomotiveI disagree. It’s not called the Andy Camel Biology channel for nothing.
I was just thinking the answer would be "as many as you can stuff in your pockets"
If I ever have a camel, 3000 bananas and 1000 km to walk then I will keep this in mind.
Wow I already thought that my idea of going step by step by one kilometer is wrong. Well in russia we call it "the quieter you go - the further you go"
I'm reminded of an old joke: "Fool, don't you know that you need MORE camels?"
3 camels would just eat all the bananas when you got there tho
@@AbsoluteHuman The original joke was about people buying watermelons for 50 cents each, and then selling them for two for a dollar, and not understanding why they weren't making any profit.
They consulted with a friend, who told them "Fools, don't you know you need a bigger truck?"
This man took a riddle and turned it into a math problem.
You forgot about the camel’s prison wallet
Can’t I just carry the 3000 bananas and have the camel carry me? That way we reach the destination with 2000 bananas.
*Unexpected event has happened*
The camel was too exhausted for continuing the trip, it died after the 400s km. Now you're alone with 2600 bananas and a task. Now you may carry at max 100 bananas every trip and have to eat 1 every km, they must arrive at a 600km distance
If it's a camel I assume it is in the desert. Those bananas are going to be rotted to nothing long before you can move them. End of riddle.
If given our current technology, I think the answer is still 0 because the bananas would probably have all rotted before the camel would be able to do all that.
Had it been an EV camel no bananas might have reached depending on the weather & season
Just *desert* the camel and carry all the bananas yourself so you dont lose any
That camel just ate 2,466 and 2/3rds bananas.
Is he going to be okay?
The explanation is interesting, but now I am wondering how you figured out you had to go back an forth 1km until 200km? What calculations did you make in order to determine it was optimal at 200km?
Stops at 200km and changes because there's less bananas no longer requiring 3 trips back and forth, only needs two trips
Don't think in terms of km but in terms of bananas. When you have 2000-3000, you need 3 trips per km because the camel can carry up to 1000 bananas. When you have 1000-2000, you need 2 trips per km, and when you have 1000 bananas, you just need a single trip. The 200 km mark is the point when you go below 2000 bananas since you sacrifice 5 bananas per km (1000bananas ÷ 5 bananas = 200 trips of 1km = 200km). Same logic from there on.
it was because the restriction of carry at max 1000 bananas at once
We're assuming it's monotone and the optimum must be at one or other extreme. There wasn't any argumentation showing that there was no better solution. For example, take 1000 bananas 200km dropping 600 and returning for the next 1000. My intuition says that most cases where you don't run out of bananas are equivalent, but if have to do it long hand to convince myself
@@stevecarter8810someone mentioned shorter increments such as .0001 km but I tried doing .5 km increments and it turned out the same as 1 km so my guess is as long as you always start trips with 1000 or whatever is left it will be 533.33333 or you won't make it.
Most Game Theory solutions ever!
10/10 for finding NE for the Camel owner which is Me according to the problem.
I first rephrased the problem: since the camel can go back and forth, it can transport 2000 bananas when eating 3 bananas per km and 3000 bananas when eating 5 bananas per km. So let it start with 3000 bananas, after 200 km 2000 are left. After another 333⅓ km 1000 are left (note the camel actually walked 1000 km in each of the first two phases, but the bananas only made 200 km and 333⅓ km progress). Now with these 1000 left it can walk the remaining 466⅔ km, which consumes another 467 (rounded up) and leaving you with 533 bananas. The camel walked 2466⅔ km to transport them.
EDIT: Note that the camel doesn't have to stop every km. Simplified tour:
Load 1000 at km 0 (0→1000)
Unload 600 at km 200 (800→200)
Load 1000 at km 0 (0→1000)
Unload 600 at km 200 (800→200)
Load 1000 at km 0 (0→1000)
Load 200 at km 200 (800→1000)
Unload 333 at km 533⅓ (666*→333)
Load 1000* at km 200 (0*→1000)
Load 333 at km 533⅓ (667*→1000)
Unload 533 at km 1000 (533*→0)
*(assuming it eats bananas before walking the 1km rather than after)
Theoretically wouldn’t that mean if you did the little return trip method with less than 1km it would be more and more efficient the less each trip was?
Time stamping this now 0:19 havent seen the answer yet, 1000 bananas, bring him halfway, you’ve lost 500 bananas, bring him back, now hes carrying no bananas since he ate them all, add another 1000, bring him 250km, you have 750 left, bring him back, you have 500 left, put another 500 leaving 1000 behind, call your friend with another camel and have him bring you the rest. But wait. Zero bananas left. Oh well
Is there a point at 2003 where you should just abandon the third trip back?
The question is "How many bananas can be transported 1,000km?"
It's a trick question, it doesn't say they have to be done all at once or how many are left by the end of the trip. The only rigid rule there is the distance and the material good.
However many bananas one has access to, theoretically an infinite amount of bananas, can be transported across 1,000km.
You know what..... you're right. It should have said: "Given the context provided, how many bananas can be transported in 1000km?"
In this case, this is the same meme as "Find X" and circling X in the problem.
The problem is in the work required by the man accompanying the camel in unloading and loading those bananas so many times
The real solution is different, but delivers the same 533 1/3 bananas.
(By real solution, I mean the most reasonable)
You move in 5 walks the 3000 to 200 km mark - creating a 2000 banana depot.
You move in 3 walks the 2000 to the 533 1/3 km mark - creating a 1000 banana depot.
You move in 1 walk the 1000 to the end - delivering 533 1/3 bananas.
I just woke up and solved this riddle in my head. Thanks for the mourning exercise. Although, as some commenters pointed out, it is more effective to abandon 1 banana at 1001. Also I don't think that you can eat fractions of bananas because in that case the smaller parts of banana you eat per turn, the more effectively you transport them... hmmm. This could make a nice calculus problem.
The first half of that trip sounds like my own personal hell.
That's all well and good but once all that potassium reaches the camel's water supply it's kaboom camel
I started counting the number of times the word "banana" (or "bananas") was said, but couldn't make it to the end before going bananas.
Now prove this is the most optimal solution 😈
Depends on what you mean by solution.
The 533 1/3 bananas at the end IS the maximum amount, but the 1 km at-a-time strategy is nonsense. It causes unnecessary unloads and reloads of cargo.
The most reasonable way is as follows:
Stage 1:
Load 1000 b's, eat 200 to go 200 km. Drop 600 b's and eat 200 to walk back.
Load 1000 b's, eat 200 to go 200 km. Drop 600 b's and eat 200 to walk back.
Load 1000 b's, eat 200 to go 200 km. Drop 800 b's. No walk back.
(Drop zone has 600 + 600 + 800 = 2000 b's)
Stage 2:
Load 1000 b's, eat 333 1/3 to go 333 1/3 km. Drop 333 1/3 b's and eat 333 1/3 to walk back.
Load 1000 b's, eat 333 1/3 to go 333 1/3 km. Drop 666 2/3 b's. No walk back.
(Drop zone has 333 1/3 + 666 2/3 = 1000 b's)
Stage 3:
Load 1000 b's, eat 466 1/3 to go 466 1/3 km. Final drop 533 1/3 b's. No walk back.
An argument can be made from this strategy to show that no better delivery is possible.
So your camel is constipated and dehydrated and your character died of starvation, nice riddle 😂
It takes 2(x-1) trips to move a given distance, where x is the number of times capacity is reached with fuel left over.
Funny to think that this kind of calculation was of utmost importanfe when coal was the most used fuel for transportation.
I hoped there would be a mathematical proof that this is the most optimal solution. Just because the total opposite is worse doesn't necessarily mean this is the optimum.
Remember eating the camel is always faster than bringing the bananas.
Want to take this a step further! Now distinguish the mathematical equation out of this so we can calculate it faster without going in this whole story
May this wisdom serve me well.
Counter solution: hire a truck that can transport 3000 bananas and pay them with the camel.
This is the perfect analogy for how the government spends our tax money. The government (camel) says go stand over there while we create something valuable with your tax dollars (bananas). Except they use the first strategy then demand more bananas when they show up, having eaten all their bananas on the journey with nothing left to show for it.
When I tried solving it I only managed to get 500 across, but now I can transport a whole extra 33 and a third :)
Thank you
I came up with (probably) the same solution to move 500 bananas 😅
I know this camel. She was very happy till 200km. Then she resigned.
I asked my physicist friend about this problem. He said imagine a spherical camel in a vacuum…
The camel would die on the way back. The first trip would take all bandanas. So none can be transported.
The solution with the least trips would be to have the camel deliver 200 bananas to 400km twice then pick them up in the last trip which would make it 5 trips total with 400 bananas left over.
I'd go 1000km with the camel with 1000 bananas, sell that camel to rent a car, and go get the rest of the 2000 bananas. Keeping that camel is a liability.
You forgot about the banana inside the bananahead trying this.
You'd assume with 1 banana left, that last kilometer would be a breeze and he wouldn't be as hungry for bananas. lol
That's bananas. B-A-N-A-N-A-S
If he can drop bananas...
900 bananas...
Drop one per km and keep going.
At 300km, he turns around.
He's wasted 600 bananas.... and now idk what.
I say the camel travels 1000km and transports 1000 bananas because its still on him just in his stomach.
My brain is too fried for this imma have to watch this again when i get proper sleep
3000 bananas, leave the camel behind and walk yourself
The ability to arbitrarily deposit bananas definitely needed to be part of the problem statement. People often won't come up with something unprompted if it is nonsensical in reality. Abandoning your cargo on the road is a good way to have it be stolen or damaged by the elements. A reasonable person wouldn't take that liberty. So it's not something you can expect people to infer as part of a puzzle.
You using miles and kilometers interchangably made this fairly confusing near the end.
By the time the 533 bananas got delivered, they were rotten from the Sahara Desert heat.
If you do the journey in increments of 250 miles you lose 33 more bananas
Move 3000 bananas 200 km (5 walks). Makes 2000 banana depot.
Move 2000 bananas 333 1/3 km (3 walks). Makes 1000 banana depot.
Move 1000 bananas 466 2/3 km (1 walk). Delivers 533 1/3 bananas
What if the camel eats 1000 bananas at starting & carry 1000 banana on him, that would gave him the energy to travel 1000 km with 1000 banana on his back. By this maximum number of bananas that can be transported is 1000.
Yup that's how camels work
I thought “why don’t I just hold a banana in my hand and make the camel carry 1k?” 😭
Surely the answer is: it's impossible. The second line says 'the bananas' which refers to the 3000 bananas on the first line. However you load the camel, once it has moved any distance you will have fewer than 3000 bananas because at least a proportion of a banana has been eaten. Therefore the 3000 bananas can't be transported 1000 km.
Little known fact: banana's are a natural food for camels.