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- เผยแพร่เมื่อ 7 ก.พ. 2025
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Smuggling yourself aboard the rogue submarine was the easy part. Hacking into the nuclear missile launch override - a little harder. And you’ve got a problem: you don’t have the override code. You know you need the same numbers that were used to authorize the launch, but one wrong answer will lock you out. Can you figure out what numbers to enter to stop nuclear war? Alex Rosenthal shows how.
Lesson by Alex Rosenthal, directed by Igor Coric, Artrake Studio.
A very special thank you to Jon Schneider and Brian Chen, who wrote the original version of this puzzle for the 2021 MIT Mystery Hunt and were inestimably helpful in adapting it to this format. You can find that original puzzle - and many more like it - at: bit.ly/MITHunt
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Well, this is definitely one of our most difficult riddles! Did anyone manage to figure it out? Let us know how you did it ⬇️
These aren't riddles, they are math problems with a story.
@Ted-Ed You just mixed number theory with Cheryl's Birthday Puzzle lol
I havent even started the video yet puhleeze
Ozo.
Oh no riddle can be more difficult than that 3 god riddle
I was scuba diving one time in the Indian Ocean and I saw a submarine with minions and a nuclear weapon being launched. I watched this video and was able to stop it. Thanks Ted Ed
Impressive that you managed to watch the video, diffuse a torpedo that used the same logic as this video and then post this comment all in the space of 10 minutes. Kudos to you man!
This is why we do what we do 🙏
The humour is strong with this one!
@I daignose you with invalid Oh, that’s me.
@@TEDEd You guys are one of the most consistent highest quality channels out there. Like Melodysheep, Kurzgezagt and Veritasium.
I think the real question is “Why would you secure 2 nuclear lock codes with a single digit?”
Cos it’s easier to remember
Cause who would be looking for single digit numbers when they're described as a code? It'd be so simple that it just becomes too simple and maybe thrown out. It's still a poor choice but there could be some logic to it.
Because it wouldn't matter either way. The system was programmed to lock when a wrong code was entered so brute forcing it wouldn't work.
Cuz the likelihood that someone randomly guess them on the first try is precisely 1 in 42
Edit:
1 in 30. I misheard the boss when he came back to the minions. And it's actually 1 in 60 if they don't have to be in a correct order.
You may be interested to know that for the longest time during the Cold War the password on US nuke silos was 000000
That boss should have thought twice before giving the codes to minions who are “expert logicians”
Especially when they don’t have the authority to disobey the boss’s orders and not launch the missile
So what I'm hearing is that at least one of the minions has green eyes?
@@Entias and they know the meaning of Ozo and Ulu?
@@Entias And that the man in the green house stole the fish?
lmao
Normally once they explain how to solve the riddle, I'm able to follow along and go "Oh, that makes sense."
This one, I'm still just as lost as when I pressed play.
Same-
This is always for me
Tbh I knew more about before i started the video
Proof by contradiction. By going through the possible results in reverse and eliminating those that would cause a contradiction in the facts, you could find the answer.
I actually had something going, then I just wanted to know the solution so I watched the rest of the video amd for a while I was more confused.
"Can you solve the rogue submarine riddle?"
I know I never can. I just enjoy the video.
This one is extra hard
I mean you could try though
Same
Me too
@@NabeelFarooquimy brain couldn't handle this riddle, and the explanation, :v
I got a little confused with the “two or more whole numbers” and went with two or more digits per code. Still had fun!
Same
me too
exactly
Yeah me too, however this way the riddle isn’t solvable
same here
So the boss didn’t want the minions to know each other’s code, but then nonchalantly tells them how to find it?
I commented something like that before I refresh and see this haha
and what kind of boss creates a Single-digit override key/password to his missile???
The boss was concerned that they'd launch without permission, not that they'd over-ride the launch. If that's the only nuke there's no issue.
Lol
That's after the launch is initiated. It doesn't matter anymore.
1:36: "6. The minions are expert logicians."
Then why are they stuck as minions?
Minions have a chance to escape when the bomb goes off. Big Bads get taken down one way or another.
Because the boss is a master logician ehe.
Diplomas aren't worth much lately, they still have to start low
Cuz the boss is 10x their size and can kill them with a single finger if they get out of line. XD
99th like
Difficulty level: master
Ah yes, becouse all of the other riddles are just too easy
I don't know, the elemental crystals riddle was pretty straightforward
@@stomyn yes, table riddles are in the lowest level, as much as Troll Paradox was.
the pearl chests takes my potato brain 10 seconds only
This is definitely one of if not the toughest
Where does it say difficulty level
I love that I've watched enough of these to recognize that the minions being able to figure out each other's answer is actually useful information. Still can't solve it, but I'm interested to see how it works in the solution.
YES SAME
I think recognizing that as useful information is kinda easy because it’s basically the only information given.
This whole riddle reminded me of that one harry potter bonus riddle
Hears the question: **confusion**
Hears the solution: **even more confusion**
The real genius here is B, he understood what A's number was in no time. He should get a rise and become the BBEG of the sequel to this video...
Sad he's dead.
@@summertriangle4745 ...Plot twist! He's not, and wants his revenge...
@@destegiovi❗❗❗
But he got exploded by their own missiles. Shouldn't have became expert logicians.
When Ted-Ed adds the difficulty level to the riddles, I know I am up for the challenge to solve them.
Hi we have same pfp😃🤗
@@aryatejc8067 bruh🤣💀🙏
@@aryatejc8067 th-cam.com/video/lg5WKsVnEA4/w-d-xo.html&6s
@@Alkalus noice😎👌
its there to scare us
This is only the baby version of the riddle. The original one goes like this:
Two perfect logicians, S and P, are told that integers x and y have been chosen such that 1 < x < y and x+y < 100. S is given the value x+y and P is given the value xy. They then have the following conversation.
P: I cannot determine the two numbers.
S: I knew that.
P: Now I can determine them.
S: So can I.
Given that the above statements are true, what are the two numbers?
Is it 9 and 18
I believe the answer is 4 and 13
@@carpediem6841 there are no numbers that add up to 4 and multiply to 13
@@cooperplant8907 4 and 13 are x and y. S is given 17 and P is given 52
I consider this version easier because you know by default there are only two numbers.
"Can you solve this riddle?"
Of course not, but I'm going to watch this anyways
Same
Hahaha... Same.
Am I the weird one? I literally never finish the video until I solve it
@@flargarbason1740 Did you manage to get the answer on this one
🤣
thank you youtube for recommending this to me based on recent events
*Puts gun to head pointblank*
"What's the code? Don't make me ask twice."
*Nuclear unarmed, world saved.*
Not really a logician's way but yeah it still works 😁
@Evelyn 21 y.o - check my vidéó Hey, delete your channel instead.
I love how everyone in Ted-ed's puzzles are expert logicians, who can solve multi step processes within minutes mentally.
The big boss is the true definition of *”When the villain talks too much about their plans”*
I was confused by what it meant for an integer to have 2 elements, when it actually meant that the set had 2 elements. And later the explanation didn’t clearly distinguish between the reasoning would lead to B knowing, and the reasoning would lead to B not knowing; I thought it was a single line of reasoning, and then suddenly we’re left with 4 options, whoa!
i love how it's incredibly complicated and takes A LOT of steps more than you think it would, when you were just playing with SUCH SMALL NUMBERS
I'm blessed with a perfectly timed upload of ted ed
Plot twist: the boss was not perfectly logical, did a miscalculation, and now you're locked out.
"I don't know if two one-digit launch codes really make logical sense as security."
"Well, remember, B, we know that we're perfect logicians, but the boss might not be."
I mean... the thing is your logic is exactly why it's a perfect code;
Nobody would expect such weak security. Force overthinking.
1:00 just your everyday conversation with your boss
*Boss after his integer explanation*
A:that’s oddly specific boss…
B:Yeah really specific…
Boss: at least my name parents didn’t name me A or B!
A+B: *SADNESS*
That’s good stuff :)
their parents named him c
I-i am D😢
LOL this is too literal with the scenario, literally the literal meaning of when "you take things too literally"
I think I solved the riddle in about ten minutes. Wasn't timing it, so we'll never know if I could've saved the world.
Genius
@@mubasshir Thanks very much. I had more trouble interpreting the English and the parameters of the puzzle, than I did the math.
I basically just worked through the first couple of possibilities, same as the video. Can't be 1+2||1x2, since it'd be obvious to both of them, and 1+4||1x4 was the first number which had all the elements needed, so it only took the fourth step of trial and error.
@@vanivanov9571 oh you went that far? I was trying randomly. 2,3 and even 4 digits. Should've been more systematic
@@mubasshir I also started with 2,3 as my first example to try and understand the logic of it, interestingly. After that, I decided to start from the smallest end of things, figuring that all I needed was two possible combinations to make the statements true, and that one should appear quickly in the low end of numbers.
Honestly, even after I worked it out I wasn't sure if I got it, since I didn't properly comprehend their explanation at the start. That's my usual problem with these riddles.
Step 1: Confirm you have Green Eyes
Step 2: ask the minions for the 2 pass codes
What is it with the green eyes by the way
@@Alexander-km2jo it's a meme from the Green eyed Kids riddle in this channel.
You'd have to watch that one to get it.
I was looking for this comment 😂😂😂
@@lancebird6675what, no it’s the green eyes riddle on this channel
edit: never mind, i read it wrong
Don't worry guys I solved this and now imma go save those people
These stories are always so outlandish and unrealistic :D It's obvious that someone finds or comes up with a riddle and then the storyline is forcibly shoehorned around it. But it's super funny to me. The riddles and the animations are always superb and the seriousness of the presentation makes the "story" very enjoable. And of course it makes it all easier to grasp too.
Boss: "I can't let my minions be able to launch the nukes on their own. I must ensure the security of my assets!"
Also boss: *makes the password to launch the nukes 2 one digit numbers."
Also also boss: **tells them how to find out each others numbers**
I love how they removed the "Difficulty: Master" part of the title
Yeah I'm no master of these riddles but I was able to solve this one in my head in about 10 minutes without writing anything down. The explanation looks pretty complicated in the video, but if you understand the problem completely you quickly realize there aren't many options to work through and they're all very simple arithmetic.
Honestly, the only good riddles on youtube
Thank you Ted-Ed for believing I ACTUALLY have the ability to solve this riddle.
I failed by the way, but I mean it was fun to watch.
being brought back here after a certain something really makes me laugh
Ted riddles are like: "so, a duck is falling from the sky into a fantasy lake that will start a chain reaction and set the world of fire, but if you manage to shout out the numeric sequence that god was thinking at the time of creation you can prevent it. Here are some incredibly random clues about said number, can you save the world?"
Its kbviously ektger 34 og 67
and i love it.
In my opinion, when B says "I know your number, and now know..." it implies that he knew A's number before A said anything. This makes sense if B has the product 4 or 5 but does not make sense if the product was 8.
If A had the sum 6 and B had product 8, he would be able to infer that A has 6 only after A has spoken and indicated that the sum must be 5 or 6. In this case, B would have said "I now know your number, and...". Therefore, A having the sum of 6 and B having the product 5 is also a valid solution as A will know that the product cannot be 8 based on the wording.
Is that tripped me up as well, If you change the order of the conversation to, I know your number, Oh I wasn't certain if you knew my number or not, You know my number now, then the outcome changes. Still I think the original answer is correct as is.
I did the same thing and got 1 and 5. I have no idea how anyone interpreted it the other way.
Actually, he doesn’t have to clarify whether he knew before or figured out from A’s statement. It’s on A to decide whether it was before or after and if he can’t decide(as in the 6 sum case) then it has to be the other one. B’s statement that A NOW knows indicates that what he just said makes clear without a doubt which one he has.
In my opinion there is no such implication. I agree that this wording would be weird in the case of A=6, B=8. But weird doesn't mean false. It is like "I know your number (and I'm not telling you whether I knew it earlier or not) and I know you know mine (and for this part of this sentence I admit I only have this knowledge after you spoke)"
I was thinking of the same thing as well. If B had a product of 5 he could deduce A's number is 6. While A doesn't know at the start if B's number is 5 (1 x 5 ), 8 (2 x 4), or 6 (1 x 2 x 3), after B says that he found A's number, A could deduce that only 5 could be B's number.
I like how the laptop is RGB, the little details
Bet it's a Razor laptop.
Ah yes, now I know not to give minions a one-digit code next time. I'll give them a 2 digit one :D
This editing is crazy good. Also I love the narration, and the riddle is very hard, not for casuals like me. If only I had green eyes...
Then we could ask to leave...
Mr Ted, in future I would greatly appreciate if in puzzles like this the characters were named something more specific than "A" and "B", and maybe if they had contrasting character designs. It's easier to follow along with the explanation if I can tell who thinks what
I got lost a little.
The boss says he chose numbers less than 7, but did he specify that the sum and product must also be less than 7?
Yes exactly. Otherwise 3 and 5 can also work.
Yeah I'm still confused as well. Also, why call them elements and not digits?
I was wondering the same, but no, I think it is A’s logic that excludes possibilities above 1x6
@@nehamotwani6477 That's what i thought at first, but 3x5 = 15, same as 3x5x1, so B wouldn't know A's number. Since the number must have at least 2 factors, it must have exactly 2 to make sure 1 is accounted for. Or at least that's how i explained it to myself.
No, it is A's first sentence that excludes all but 1xP P Prime and 1xN^2
This one is actually hard, one of the few on this channel that I didn't managed to solve right away (but I did get very close). I have a feeling that the number must be very small and there is only 2 number in the set (otherwise there will be way too many cases to consider). Then, I realize that the set must have 1, because otherwise B wouldn't possibly know the answer even if it can be factored (i.e, if B's number = A x B, the set could be (1, A, B) or (A, B), which result it different sums). After this, I only tried found (1, 5), and it seems to be working.
After watching the solution, I know (1, 4) works, but I still don't understand why (1, 5) does not work. A's statement is quite self explanatory: when A knows he has 6, B could have 5 (1x5), in which he knows A's number (even before A say anything). B could also have 8 (2x4, 1x2x4) or 6 (2x3, 1x2x3), in which B cannot tell A's number. So A knows that depending on B's number, B could know the underlying set, which gives A's number, or B could not. So he said "I don't know if you know". B's first part also works if B has 5=1x5. However, B knows A will know the underlying set after he said "I know your numbers". This is because he knows A has 6, which can has product of any of 5, 6, 8, and B has 5 is the only possibility that B would know the set (and thus A's number). This means if we separate B's statement (i.e., suppose B said 2 sentences and A comprehend them sequentially), it actually works.
Exactly, I was looking for this comment
If the sum was 6, a product of 5 (1x5) or 8 (2x4) would also tell B that the sum was 6. The reason B can conclude the sum is 6 (when his product is 8) is because he knows 1x2x4 can't be a combination, since their sum is 7. If their sum is 7, A would know for sure that B wouldn't be able to figure out A's number, since all the 7 combinations (1+2+4, 5+2, 4+3 --->> 1x2x4=8, 5x2=10, 4x3=12) wouldn't allow B to narrow down and figure out A's number. Thus B knows that a sum of 7 would contradict A believing B could figure out his sum.
I followed a similar logical path and narrowed it down to (1,4) and (1,5) myself... thought about it for another 10 minutes and couldn't really get anywhere.
This is probably the hardest solution I’ve heard from these riddles. Like I usually understand the solution when explained but I’m even more confused now after hearing it.
I'm pretty sure the wording is just not clear enough. When this many people are commenting about being confused you've gotta think that's a flaw of the video
I was quite close, but tripped up by 1:20 "B thinks this over."
If B's product is 4, then the information A presents is actually irrelevant -- B immediately knows A's number, as 1x4 is the only possible way for this to be the product, and 5 must therefore be the sum. But B "thinking this over" got me into the headspace that A's information was NECESSARY for B to know A's number.
I came down to 5 & 4 or 6 & 8, but went with 6 & 8 because of this trip-up. Argh...
There are difficulty levels now?!
I probably still can't solve baby difficulty riddles...
Where does it say the difficulty level??
@@mediocre_guy the title got changed.
I think I've got another solution by thinking about missing numbers from the set of (1,2,3,4,5,6) instead.
- If the boss choose (3,4,5,6), then A has 18 and B has 360.
- A will not be sure if (1,2) or (3) are missing, while B will not be sure if (1,2) or (2) are missing.
- However if only (2) is missing, A would have had 19 and A would immediately know the boss set. (There is only one set that sum is 19.)
- After A stated that 'I don't know', B now knows that (1,2) are missing and A got 18.
- After A knows that B knows, A is now certain (1,2) are missing and B got 360.
- Because if (3) is missing instead, B would have got 240, which means B are not sure if (1,3) or (3) are missing, which means B are not sure if A has 17 or 18, but each number does not have unique set like 19; 17 could be (1,2,3,5,6) or (2,4,5,6) while 18 could be (1,2,4,5,6) or (3,4,5,6).
A gets 18 and knows that B has either 240 (1,2,4,5,6) or 360 (3,4,5,6). In both cases, B doesn't know A's number (you explained the reason already). This means A knows that B doesn't know their number. That contradicts A's Statement.
@@cheshire1 Actually no. If B has 360, he would know A would have either 18 or 19. If A got 19 he would immediately know B's number, because it is the only combination with that sum. So B concluded that A has 18.
@@kaienumino1811 No one said that A doesn't know B's number, so B can't use that to rule out 19.
@cheshire1: wrong. A says it does not know Bs number
Oh hey, a new riddle!
Not that I can solve it on my own, I just like to see the story behind each one lol
So many comments say TED-Ed presented the problem wrong or left out info, like:
"they meant the sum is smaller than 7"
"you only add/multiply 2 numbers"
"sum and product only 1 digit"
etc.
1+2+3+4+5=15 is a valid combination by the first rule.
The problem is explained well, the solution isn't:
The hard part of the puzzle is the first step, where any combination of more than 2 numbers and combination of numbers that does not include 1 is disqualified.
A says B might know his number already, so the product cant be a combination that has at least two of 2, 3, 4, 5, 6, since it could be written with or without the 1.
Example: 30=1x2x3x5=2x3x5. So if A had 1+2+3+5 or 2+3+5 he'd know B CANT know his number.
Only numbers written 1xp (p Prime) or 1xN^2 remain.
O! Now I've got it. Thank you.
@@jmugwel ^^ Glad I was able to help.
The solution isn't just explained poorly, it's also incorrect insofar as it leaves out 5 and 6, produced by the set (1, 5).
@@starseeing Assuming the set would be (1,5), A would have 6 and B 5.
From the sum being 6, A can't know if it is 1+5, 2+4 or 1+2+3. Check.
From the product being 5, B knows it is 1x5. Check. B knows A has 6.
But A still does not know if B's number is 5=1x5 or 8=2x4, contradicting B's statement that A knows B's number now too.
@@MasterM23 I would think that A knows perfectly well that the set cannot be (2, 4), as B wouldn't claim to know A's number if (2, 4) and (1, 2, 4) were both possible for him.
The piece where the boss comes and tells the information needed by the protagonist reminds me of so many films ;)
I’m so happy :))) This is the first Ted riddle that I managed to solve in my head without the use of scratch paper!
Wow! Amazing! You must be a mathemathics and game theory genius to be able to solve a puzzle like this and not the other simpler ones (e.g. bridge riddle). And you're solving it all in your head, without any scratch paper, something that even the most trained logicians couldn't do.
I misunderstood the riddle. I thought the sums and products could be greater than 7, but the numbers comprising the sums/products couldn't be greater than 7. I might have made it harder on myself. Oh well, too late, I looked at the answer.
Same
Actually products and sum can indeed be greater than 7 it's not necessary for them to be less than 7 but here for sum or product to be greater than 6 contradicts statement of B that he must know the sum. But, I'm not sure about this though as few other people also have answer more than 7. Needs deep inspection.
@@ashutoshmahapatra537 18 and 360 satisfy the conditions
Sum and product could be greater than 7, but when A starts by saying B might know his number already we know it has to be 1xP, P Prime or 1xN^2.
@@outdoordannyd A says B could already know the answer with his number, but for 360=6x5x4x3x1=6x5x4x3 so B could not know his number.
I think this is the first time that I was both unable to solve the riddle, _and_ unable to grasp how the solution was deduced
Alright so I'm gonna be honest here chief these are usually fun little brain teasers but right now I've heard the thing explained to me about 4 times already and the only thing I'm feeling is my brain dripping out of my ears.
This is probably one of TedEd's hardest puzzles, and yet I figured it out in about a single minute (and lying in bed before sleep), yet I had failed to figure out dozens of much easier puzzles before this. Funny how our brain works! The clue for me was that the boss's two original numbers were distinct, so 1 and 4 are good numbers because their product (4) can only be made in a single way (since 2 and 2 are duplicates). 1 and 5 would add up to 6 which could, however, also be a factor of 2 and 3 so the other minion wouldn't have been able to narrow it down like he did. So the originals must have been 1 and 4.
Hits different in 2023
You should do more riddles!
In fact, there are two valid solutions to this puzzle.
A set of at least two distinct positive integers that are less than 7 means that pairs, triplets, sets of 4, sets of 5 and a set of 6 are considered (1,2,3,4,5,6). These add up to 57 possibilities for the set chosen by the boss.
When A says: I don't know whether you know my number, that eliminates only 2 possibilities (1,2) and (1,3) (as per the video)
When B says I know your number, basically, they say the product of the numbers in the set is unique, that is 1, 2 ; 1, 3; 1,4 and 1,5. The first two have already been eliminated at the previous step, therefore the remaining ones are valid solutions: 1,4 and 1,5. Why is 1, 5 valid?
The video states that if A had 6, they wouldn't have known that B had 5 or 8. But that's not correct, because after B says I know your number, A knows that there are only two possibilities left, and A also knows their own number (which we do not), meaning that if A had 5, they would now know B had 4; and if A had 6 they would know B had 5.
In other words, B's statement "now I know you know my number too" is valid whenever there are distinct options available (in this case 2)
So the valid codes are (A,B): (5,4) and (6,5) meaning that unfortunately we would have to make a guess with 50% probability of success to crack the code.
Totally agree. I think Ted Ed made a blunt here.
Thank MasterM’s excellent explanation. Ted Ed needs to remake this video.
It spent too much effort to explain how hard the logic process will be but did not clarify the ambiguity inside B’s statement or make the reasoning process more understandable.
18, 360 also works. The set would be (3, 4, 5, 6).
@@starseeingusing the logic above, 360 won't work because it has two possible factor sets, and so B would not know A's number
I wonder why you only got 3 upvotes (including mine) after 2 years.
I have a much simpler solution:
1. Confirm you have green eyes
2. Get into House Minotaur
3. Escape the 3 alien overlords
4. Confront the 2 minions & challenge them to a wizard duel
4.5. Use the worst wand available & miss
5. Once defeating the minions, ask them to stop the missile for you
Is this puzzle has a bug or someone has the answer ? Why can't A=6 and B=5 be the second answer ? Since 6= 1+5 or 2+4 or 1+2+3 and now switch it to B's side, 2*4=8 and 1*2*3=6 (Which 8 :"" 1*2*4 or 2*4 "" and 6: "" 1*2*3 or 2*3 ""can't be B's answer. Because if they are B's answer then he wouldn't sure what A got) Therefore, the moment B says "I know your answer" A can figure out B's answer is 1*5=5.
Because B knows that the sum should be either 5 or 6. Otherwise, there are no way that B can guess the sum with his number and this would mean that A should've say "I know that you don't know my number".
I agree with you Sam! In any case, if B says that he knows A's answer, A can conclude that the only way for B to do so would be 1,2 1,3 1,4 or 1,5. Since A did not know the numbers at first, we eliminate 1,2 and 1,3. So whether A get a sum of 5 or 6, A will know B's number the moment B says he knows A's number.
Okay oops actually there is no second answer but the video did not explain it clearly. Basically what asdf123 is right. If the sum for A is 7, A will say that there's no chance my number can be known (you can write out the cases and you'll see). Which is why the dilemma of 2,4 and 1,2,4 does not exist; B will know straight away that 2,4 are the right numbers. Hence from A's perspective, A would not know if the numbers are 2,4 or 1,5.
Let's all agree that the 2 guys with the codes, and the guy that cracks the code are the quickest thinkers in the world.
This was tough, especially the part about decoding "I don't know whether you know my number"!
I solved it. The possibility of 1 being one of the numbers in the set poses a problem for B: he can not know if 1 is there or not UNLESS the set consists of 2 integers and one of them is 1. In all the other scenarios 1 could be a factor in B’s product without B having any information about it. B would not know if A’s number is X or X+1. But B does know: therefore set is 1 and one other integer.
Rule 1 REALLY needs to be reworded. I needed to see part of the explanation and then re-read it a few times to link it as a "set with at least 2 elements". Initially, I was trying to figure out how the numbers "had" 2 elements and what those "elements" even were. I was also confused as to what subject the "In other words" was rewording - the whole rule or the "elements" part.
Either keep only the "In other words" or change it to "chose at least 2 distinct positive integers".
True...
I confused the rules, so I arrived to the conclusion of "7" (5+2) and "10" (5x2) for "A" and "B" respectively, which actually would be true if the rules said that the 2 Codes are the Sum and the Multiplication of *only two numbers* (I missed the "at least" part lmao) different each other and lower than "7" for "A" and "B" respectively.
It bothers me because I know I'd have been able to solve it if I had all the rules clear (since I followed the same reasoning as him to solve it), but I now don't have any empirical way to prove it 😔
The statements are equivalent to "The sum fits at least one product with multiple possible sums, and also fits exactly one product with just one possible sum. The access code is the one where the product fits just one possible sum."
I think it helps to list the possible products on one side and possible sums on the other and connect those that fit.
Teacher: The test isn't that hard
The test: 1:30
Too bad people on the Titan submarine didn't know such override code
💀💀💀💀
this follows the same sort of logic as the bonus harry potter "how many times did you watch the titanic" riddle!
why don't they ever show the answers to the bonus riddles without you paying ACTUAL MONEY?
I’m kinda proud of myself for nearly solving this problem. I used a different approach but narrowed it down to 6 answers. And then I chose 1 x 6 like a dunderhead. It was 5 in the morning and I was doing it in my head, and I was getting frustrated with the riddle. I had 1 x 5 and 1 x 4 on the list but I just ignored them for some reason.
I solved this using excel (to be quicker).
Listed all the possible combinations of numbers 1to 6 without repeating digits (there's 57 combination), then calculated the sum and product of the digits. Looked for the non duplicate values in the product column that had a duplicate value on the sum column, and voila the sum is 5, the product is 4 and the seed digits are 1 and 4.
I think you got lucky. The sum also needs to be connected to a duplicate product (else A would know that B knows their number) and it can't be connected to a second non-duplicate product (else A wouldn't know which of them was B's number after B's statement).
Oh my God I am so obsessed with your videos I started watching this channel since kindergarten and ever since I am obsessed!!!!!!!
Wait, you had the power to send the submarine to the bottom of the ocean all this time and decided to solve a logical puzzle instead?
Im sorry to do this! But this problem has two solutions. TED Ed missed the fact that this riddle is unfortunately unsolvable, since having two solutions means you still dont know which one is the case (risking typing in the wrong code). Second solution would be:
Numbers 1, 2, 3, 4, and 6. The sum of these is 16 , and the product is 144. Minion A would still state "I dont know if you know my number" because there are two ways to get 16: 1,4,5,6, and 1,2,3,4,6. But both of these have different products, 120 and 144. Because there are TWO ways of getting 120, (1*2*3*4*5 and 1*4*5*6), that means that Minion B's product must be 144, otherwise making his second statement false.
But there are also two ways to get 144 as a product (1 can always be a factor), so B wouldn't know A's number
Everybody's talking about how the boss spelled out the solution for finding out the launch codes for his minions, but can we talk about that both launch codes were single-digit numbers?
One thing that I found ambiguous was B saying "I know your number", instead of "I NOW know your number." Because "I know your number" could also mean conversationally that B knew A's number before A's statement. But given either interpretation was able to solve!
I don't think this is explained well by the video, so let me see if I can do better.
First, let's look at things from Minion B's perspective. The only ways Minion B could definitively know Minion A's code is if his code only had one set of factors below 7 (that doesn't have repeating numbers). In other words, Minion B would automatically know Minion A's code if Minion B's code was any of the following:
2 because 1x2 is its only set of factors without repeats.
3 because 1x3 is its only set of factors without repeats.
4 because 1x4 is its only set of factors without repeats.
5 because 1x5 is its only set of factors without repeats.
All other codes which Minion B code have: 6, 8, 10, 12, etc. all have multiple sets of factors without repeats, and thus Minion B's code were one of these, he would not automatically know Minion A's code. For example, 6 has 1x2x3 and 2x3. 10 has 1x2x5 and 2x5.
Now, let's look at it from Minion A's perspective. There are some codes which Minion B can't ever have, and Minion A knows this. For example, Minion B can't have a code of 7, because the only set of factors for 7 is 1x7 and 7 is not a valid element (as the rules say all elements must be distinct and below 7).
Since 3 can only be gotten by adding 1+2 (as all elements must be distinct, positive, and whole), Minion A would know Minion B's code is 2 if Minion A has a code of 3.
Since 4 can only be gotten by adding 1+3 (as all elements must be distinct, positive, and whole), Minion A would know Minion B's code is 3 if Minion A has a code of 4.
Given the above information we determined from Minion B's perspective, they would both be able to figure out the other's code without any input from each other in either of these scenarios.
By Minion A saying "I don't know whether you know my number", he is really saying "It is possible you already know my code because my code is the sum of adding 1 to either 4 or 5. However, it is ALSO possible you don't already know my code because my code can be the sum of adding OTHER numbers, too!" or simply "My code is 5 or 6."
If Minion A's code was 5, it could be gotten by if the elements were 1+4 or 2+3. Minion B's code would then either be either 4 (1x4) or 6 (2x3) respectively.
If Minion A's code was 6, it could be gotten by if the elements were 1+5, 1+2+3, or 2+4. Minion B's code would either be 5 (1x5), 6 (1x2x3) or 8 (2x4) respectively.
In other words, we know that Minion B's code is 4, 5, 6, or 8.
Minion B then begins his response with: "I know your number..." Minion B would NOT know Minion A's code if Minion B's code was 6, because both possibilities for Minion A's code are still possible in that scenario. Thus, Minion B's code is either 4, 5, or 8.
If Minion B's code was 4, it only could be gotten by if the elements were 1x4, and Minion A would have a code of 5 (1+4).
If Minion B's code was 5, it only could be gotten by if the elements were 1x5, and Minion A would have a code of 6 (1+5).
If Minion B's code was 8, it could be gotten if the elements were 2x4 or 1x2x4, and Minion A would have a code of either 6 (2+4) or 7 (1+2+4).
In other words, we have 4 possibilities:
A=5, B=4
A=6, B=5
A=6, B=8
A=7, B=8
Minion A already covertly indicated his code was either 5 or 6, so the last one is eliminated.
Minion B ended his response with: "...and now I know you know my number too." If Minion A's code was 6, the second and third options would both be possible, and Minion A would not know Minion B's code. Since Minion B indicated that Minion A knows his code, we can deduce that the first option must therefore be the correct option. A's code is 5, B's code is 4.
Thanks
Thanks!!
5 and 2 with A=7 and B=10 also work by this same method
this was really helpful thank you
@@flargarbason1740 A says B might know the answer already. If A has 7=1+6=2+5=3+4=1+2+4, he knows B has either 6=1x6=2x3, 10=1x2x5=2x5, 12=1x2x6=1x3x4=2x6=3x4 or 8=2x4=1x2x4. None of these 4 numbers would let B know what A has, which contradicts his statement.
This was probably the most confusing riddle I've ever watched on this channel
Bad time to reccomend this TH-cam, bad time
I love how the big boss was just rambling x2 speed about math-related stuff and I couldn’t understand a single thing, but minion B was like: “Oh now I know your number and you know mine too!”
This riddle requires you to know what *"the elements of an integer"* means, which I do not know and this video did not explain.
It took me a while to figure this out, but it's the set that has elements, not the integers. It would have been more clearly stated as "The boss chose a set of at least two distinct positive integers, each less than 7."
Ted Ed please post more videos about
-Aristotle teaching Alexander the Great
-Aristotle works (metaphysics,four causes,potentiality and actuality)
-Presocratic philosophers
-Islamic golden age (discoveries,achievements)
-Tengrism
-Islamic golden age (philosophers)
-Ottoman Empire astronomy
The rules for this one did not mention that the numbers the boss provided were under 7, they only mentioned that the elements of the numbers were under 7, not the actual product or sum. This led me to see that the only way they could each know which number they had was 21 and 720. Because in the scenario described you can have at least 2 elements. So the only way to be certain is to have all of the elements under 7 non repeating. Something like 123456.
3 (1+2) and 2 (1x2) would also work for this.
It is exactly my point. Initial information aren't complete
I always enjoy watching these, I get completely left behind as soon as they start talking about how to solve the puzzles. It’s fun being clueless but trying to follow along.
Ah yes 1 digit nuclear code
I exhausted all the possibilities when I solved the puzzle, and I'm pretty sure there's another solution: 8 and 15
Clearly you are suggesting that the integers were 5 and 3. The problem is that minion b would have no idea if the numbers were 3 and 5 or 1, 3 and 5.
Question: Why would the boss even consider that random fact about the numbers to be worth sharing or considered as “funny story”?
Several questions:
1. At the beginning of the video, it said we need the same two numbers but the result is different.
2. One of the boss requirements was each distinct positive integer less than 7 but the answer tends to find a number which sum or product less than 7.
Maybe I misunderstand somethings because my English is not very fluent. Please explain to me.
I got the same confusion
The numbers you need (5 and 4) are the same as the ones that the minions used (5 and 4).
That the sum and product were below 7 was just coincidence, it wasn't a requirement. Only the distinct postive integers need to be below 7.
It is worrying that 2 perfect logicians agreed that launching nukes to cause chaos was the correct thing to do
The wording of this riddle really busted me. I was thinking each minion had a different two digit code and I was trying to work from there
Is it just me or their boss wanted to be a mathematician, but ended up in the criminal world?
You mean Moriarty?
I see the MIT Mystery Hunt is now responsible for one of the hardest TED-ED riddles.
Step 1 : Confirm you have green eyes
Step 2 : Ask the green minions to give you the code
I'm Sorry
This isn't funny anymore.
The fact that they told us the answer in less then 10 minutes with full explanation is just…
*chefs kiss*
When you don’t understand the problem. Watched it. And had yet to understand it anyway.
Had a bit of trouble in this one, because rule 1 says that he chose integers less than 7, but never specifies if the sum or product also needed to be so. Following all the same logic, I came up with (2,5) for the set, which I THINK still fits the rules?
i also think the sum and product did not need to be less than 7, and waste my time more than needed
The sum and product can be more than 7.
(2,5) doesn't work, because A would have had 7=1+6=2+5=3+4=1+2+4, he knows B has either 6=1x6=2x3, 10=1x2x5=2x5, 12=1x2x6=1x3x4=2x6=3x4 or 8=2x4=1x2x4. None of these 4 numbers would let B know what A has, which contradicts A's statement, saying B might know his number already.
By the way Ted ed Team it’s been ages since you uploaded riddles🌺you should release them more often, thanks🤩
I misheard and thought it had to be EXACTLY two factors, and got 7 and 10 for the codes.
1. A has 7, which could be 1+6, 2+5, or 3+4.
2. B has 10, which can only be 2x5 (with the restriction of exactly two factors) so he knows A has 7.
3. A knows that 6 could be either 1x6 or 2x3, and 12 could be either 2x6 or 3x4, but 10 can only be 2x5.
Of course, throw in the possibility of, say, 1x2x5 and the whole thing falls apart.
5:55 wait... did i just kill minions A and B? rip
Congratulations! You solved the riddle! You monster.
I didn’t absorb a single word of that, but I enjoyed every second.