In addition to silence, we also edit out overly long explanations until they're more succinct and times I follow a confusing train of logic that leads nowhere. Is this what you expected?
The “phi” function for level 58/61 is actually the answer of the Josephus problem. It is explained really well in an episode by the TH-cam channel numberphile and I highly recommend watching it for anyone who is curious
Wondering if you would be comfortable using a timer for other puzzle games, but I reckon it's a bit distracting for you. It only serve as occasional 'wows' while most of us are satisfied with just your puzzle solving + commentary. What I meant to say is, timer is not essential and do it if only you want to tylerrr
oeis org (apparently I can't post links) is your friend for this. In the case of the first one you had trouble with, it's the solution to the Josephus problem (A006257 on OEIS) The next one is Tribonacci (add the last 3 instead of last 2, with the first three being 0,1,1), A000073 on OEIS After that is literally the sequence of numbers whose digits add to 18, A235228 on OEIS (interestingly this one ends at 963, just like the game did) the next one is the sum of the squares of the first n primes, A024450 on OEIS then the octahedral numbers (A005900 on OEIS, though interestingly it follows the floor of the sum of the first n^2 square roots until the ninth term, which is 345 there; the difference between the 2 sequences grows slowly) note the octahedral numbers start with 0 at 0, so the nice formula of n(2n^2+1)/3 needs to have the ns replaced by (n-1), which does give the same formula you calculated. There's actually a quick trick if you know the 0th term of a sequence and have calculated the difference sequences, mathologer's video on "Newton's calculus of "what comes next"" does a great job of explaining.
Seeing the timer was very enlightening, I've learned that A) I should not beat myself up for not being able to solve them quickly enough to keep up with the video B) Tyler spends *way* more time just doing the recording for these than I thought, not including editing, streams, and socials Thank you for doing your best to always put out daily uploads Tyler! Love your videos and all the cool puzzle games you've introduced me to over the years.
Yeah. Figure a 30 minute video is 90 minutes of recording cut down. And editing takes twice the raw time. That is 4 hours 30 minutes of recording + editing. So 9x the content length to produce.
no fucking idea how he does it, i didnt even know he did daily uploads until i joined the discord server. especially with the quality and length of the content he produces, it's fucking insane.
But he has an editor (as far as I remember) and the longer you work together, the less you have to clarify. Plus you can record several videos in one session.
This is all fairly expected for me. Honestly I was kinda shocked how little was cut. Second: Tyler is actually really smart. I am impressed with myself when I can solve it at the same time as him. But there have been times he has come out of nowhere with a massive brain solution, and as such I will never feel bad I didn’t get it along with him because he is genuinely really smart
For those that are confused about the wack sequence for problem 58, it’s the Josephus problem. The sequence of 1,1,3,1,3,5,7,1,3,5,7,9… is obtained by doubling the remainder and adding 1, where the remainder is the input minus the largest power of 2 below it. So y=2R+1, where R=x-2^n, where n is the largest power less than x. This function tells you the “winner” of people in a circle who remove the number to their right. In a circle of 5, 1 removes 2, 3 removes 4, 5 removes 1, 3 removes 5, 3 wins. In the function it looks like R=5-2^2=1, so y=1•2+1=3, hence why the input of 5 gave 3. In short, it goes up by 2 each time until you hit a power of 2, where it resets to 1.
You wouldnt think a calulator would be this complex, but when you have 2 strange functions and missing numbers while you always have to get 666 is pretty hard (thankfully they gave the player a non cursed calculator)
They are also kind of encouraging you to use OEIS which trivializes half of the puzzle. However, that's how real science works, you take whatever you can. I had an university professor who at that time was 70 something and I was politely complaining that his homework exercises were kind of too hard and he answered yes, they are, but you also have Google search. Learned more from that single course than all the others combined that year.
That post it note... back in high school, I would try to do that kind of stuff for fun by hand. I always performed really well in math classes, and I knew when to pay attention, so my teachers were okay with it.
3:46 Josephus problem! Here's my solution that I came up with back when I learned the problem existed I = input and O = output (I-2^m)2+1 = O When m = n-1 When 2^m < I < 2^n
8:50 "... which we all know to be..." No tyler i have no idea what the hell is going on, still loving it is always satisfying watching tyler solve this things
You kinda figured it out with level 65, but the game allows you to manipulate the result of equations after you've hit enter. It will even allow you to complete the level if you get 666 after using all the functions without clearing. You can see which functions you've used by seeing them light up. Loving the content!
4:49 there's a numberphile video on this one... the josephus problem! a way for many soldiers to suicide. one doesn't want to. how can that guy survive? the method: each soldier kills the one next to him, and the one next to that one kills the next alive one next to them. repeat until last one standing. example with 8 soldiers: 1 kills 2 3 kills 4 5 kills 6 7 kills 8 1 kills 3 5 kills 7 1 kills 5 1 is last to surrender and/or suicide.
4:47 - I believe it's the Josephus Problem. Or, the input is the number of people, the output is the winning spot in the Josephus problem. The Josephus problem is about a man named Josephus and 40 other soldiers being taken prisoner but I kinda forgot what happened. So what happens is that all 41 people are stood and ordered in a circle from slots 1 to 41. The first person must start it. Person 1 kills Person 2, Person 3 Kills Person 4, and this goes on - a living person must kill the next living person on his turn. The last person alive will be The goal is to find what number Josephus must be in the circle so that he is the last one alive. For a problem like this, it stands to reason that every even number slot will be killed off instantly. For a group of 2^n people, the winning slot is always slot 1 (which is why in the calculator, each time Tyler inputs a power of 2, it's always 1). For any group of people of size 2^n + l where l is any positive integer, the winner is always 2l + 1 (you can prove this yourself). For example, let phi(x) be the function for the josephus problem. - phi(4) = 1. Proof, 1 kills 2, 3 kills 4, 1 kills 3 so 1 lives. - phi(12) = phi(2^3 + 4) = 2(4) + 1 = 9. Proof, 1 kills 2, 3 kills 4, 5 kills 6, 7 kills 8, 9 kills 10, 11 kills 12, 1 kills 3, 5 kills 7, 9 kills 11, 1 kills 5, 9 kills 1 so 9 lives. So for any group of people N where N can be expressed as 2^n + l, the "winning" slot for the Josephus problem is always 2l + 1.
I actually recognize the phi sequence on Level 58 (3:30)! It’s the solution to the Josephus problem when starting with n “players.” I recommend looking it up if you like cool math puzzles/sequences!
Hey Tyler, not sure if you’ve been watching updates for the games you used to play, but I noticed that Luck Be a Landlord is officially releasing very soon and it just got a final “Landlord” boss. Love the content as usual can’t wait to see more!
At 10:25 I think that it is actually concatenating and then doubling each digit with carry over. So for 12 fork 5 Concatenate - 1 2 5 Double each digit - 2 4 10 10 carries the 1 to the tens place to become 250
Mental Break question @24:00 : I suspect this is what the memory buttons M1 M2 M3 come in handy for - remember that you can use it to tap into burning numbers you can't otherwise access, thereby reducing the cognitive load. =)
Keep in mind, at 14:42 the clock just passed 30 minutes and the the video is 32 minutes long. The editor managed to cut out ~20 minutes already and that seems insane to me
Btw, using the calculus of finite differences would have sped up the last part considerably. It allows you to treat the difference operator very much like the differential operator. And thinking of it that way makes it easy to come up with the formula, since you are simply integrating 4 a few times.
If anyone was wondering, the solution to level 62 is tribonacci numbers. Instead of adding the last 2 numbers, you add the last 3 - so with the starting sequence 1, 1, 1, you get (1+1+1) = 3, then (1+1+3) = 5, then (1+3+5) = 9, then (3+5+9) = 17 etc etc
Honestly I would love to see Tyler explain more stuff like the end of the video. I’m in calculus 3 and this is the first out-of-classroom experience I’ve had that actually uses derivatives in an interesting way Great vid!
this was a fun video, I think this format works great for these more "difficult to figure out but easy to execute" puzzle games, where at first glance it looks like you just fly through the game.
"Hey guys, Timer here! And today I'm going to use myself to guage how quick this mere human can calculate the number 666 in this cursed puzzle game!" Great video as always!! Love the editing on this video and the other recent ones as well!! :D Especially during the intros!
I was also trying to figure out the equation for the last phi's function and I took your sequence (from 29:20) and tried doing a Taylor Expansion assuming the first value was x=0... That wasn't a valid assumption because x=1.
Having good mental arithmetic and being good at maths as a subject are two separate skills. You have both. as someone who is doing physics at uni I followed the last part but was amazed at how you could work out 64 squared in your head
only tyler could make this game interesting enough to make a video on it. I've said this before and I'll say it again, tyler, you are one of the best youtubers out there. not only are you one of the smartest puzzle solving youtubers around but you can make any video entertaining to watch
At level 58, the Phi function was simply all odd numbers before the next power of 2. So 1, then 3 is bigger then 2^1 so it resets, then 1,3, then 5 is bigger then 2^2 so it resets, then 1,3,5,7, then 9 is bigger then 2^3 etc... It is ssociated with a problem where a group of n knight each kill the one to the right of them one after the other, and the last one standing is the value of the sequence.
Wow, Tyler has some serious math chops! I'm impressed, and I'm no stranger to scary-looking math. Kudos to you for busting out the big guns for this one, even if it didn't help you in the end.
I love that Tyler used finite differences to figure out it was a cubic polynomial, but at that point wouldn't it be easier to use regression to find the polynomial itself? With known x and y values you just need to solve a 4x4 linear system. Well, that might also take a while if you are doing it with a pen on sticky notes though :/
That was awesome!!! You made math look really fun, it’s been a while since I’ve taken out a piece of paper and tried to calculate a massive function by hand.
So fun fact: Tribonacci numbers exist (same as Fibonacci numbers except you add together the THREE previous numbers. It starts with 0, 0, 1 (with the first 0 being index 0, and the 1 being index 2), so the rest of the sequence goes 0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, ...)
goddamnit tyler, that ending absolutely broke me LMAO also 14 Minesweeper Variants comes out today! I'm excited as fuck to see your videos on the full game, ive been absolutely addicted to minesweeper since these videos came out
Could be wrong here but I’m fairly certain that last equation he made is just an integral of 4 with constants added. Or the derivative of the last equation is 4 if you will.
I frequently try to create specific equations from just a graph. For example, I once made a function where it was the integral of the absolute value of the cosine of x. My goal had just been to make a function where it was a wave that only went up.
Looked up the sequence in that last puzzle in the OEIS and the definition is wildly different than what you came up with. But your solution also works. Just shows how math is weird.
Level 63, the fork option stumped me for ages. I finally stumbled upon the solution you used, but it was blindly throwing numbers at it until 52 came out. When you tested it with lots of 1 fork # I was finally able to see the pattern. This is so fun!
Spoilers for a few functions that Tyler never actually solved: 10:30 The operation here is concatenate first, then double 12:46 The sequence here is similar to the Fibonacci sequence but it always adds the last 3 numbers instead of the last two. It starts with phi(0)=0, phi(1)=0, phi(2)=1 and the missing phi(4)=2. 26:55 phi(n) is the sum of the squares of the first n prime numbers. Check the differences phi(n+1) - phi(n) to see the pattern more easily.
3:30 I believe the function is the solution to the josephus problem, numberphile has a great video explaining the setup and the math behind the pattern.
Love this series, Tyler's math and pattern recognition is amazing so its not boring at all Tyler missed some patterns because its very hard, and not really needed to solve the puzzle lvl62: the 'tribonacci series', adding last three terms, 0 1 1 2 4 7 13 24 44 81 149 ... lvl65: sum of squares of primes 4 4+9 4+9+25 4+9+25+49 ... lvl66: not enough information lol, wth is that XD
I think we bullied Tyler into the timer shtick with comments about the editing making him just seem like a genius, which is still possible tbh, but I don’t think anyone was doubting to begin with, just jokes. Cool to know that Tyler’s puzzle ace-manship holds up, but dang I hope it didn’t get to him. Hope not.
Fun fact, the phi function in level 58 is actually the same sequence that solves the Josephus Problem. Numberphile has a fantastic video on it, but the general gist is N soldiers are stood in a circle, who don't want to be captured, so the first soldier kills the second, third kills fourth, etc, going around killing the next alive soldier until only one is left. The question is what position to stand in to survive. The answer turns out to be 2L + 1 where L comes from L = N-2^x and L < 2^x (basically, find the largest power of two in the number and subtract it)
an elegant way to describe the powers of 2 thing is the Josephus problem. it's the one with all the prisoners in a circle killing each other, and to solve it you prove that for n+1 prisoners, the survivor spot moves by 2 places. this can be proved by saying the prisoner number 1 (who kills first) kills 2, and the 3 becomes the new 1, making it equivalent to the case with n except every index is +2, with the obvious looping if 2n+1 exceeds n. in other words it's 2n+1 mod 2^(1+floor(log2(n)))
Tyler! I love your vidoes and really enjoy the fact that you upload everyday. I watch every singe one. Thanks for being awesome! Like and subscribe peeps!
its incredible to watch him just math shit out while understanding everything but still having absolutly zero idea how he can figure things out and do math in general so fast
oooh yeees!!! KEEP DOING THIS! I always wanted to know this I don't know why I never suggested this. Man that was soo obvious! But that's what I always say, until you think of something for the first time you never thought of it before.
Tyler ,regarding the "powers of two"/"odd numbers" pattern, you might want to check out the Josephus problem. It's used in that, I think (or it's damn similar), and frankly there's some videos/web apps online that are hype in explaining it
Well, that was a lot of math for math's sake. Which is sad, but cool that you can actually do it. Even with a degree in mathematics, hell if I could ever know how to get an equation from that sort of sequence. I'd probably never even work out what level of equation it is.
The fork in level 61 concatenates (squishes) the number _before_ multiplying by 2. But the order only matters in some scenarios (paricularly when the second number gains a digit when doubled), which is why Tyler got so confused.
Idk why, but the series at 3:52 reminded me of the Josephus problem, where for n number of people where is f(n), the seat that “wins” numberphile (hope I got that name right) did a solid video on it, it’s pretty interesting
You actually make me question my own smarts, I don't think I'd ever be able to do any of that math, let alone in an hour and a half. More respect to ya though, I like how you explain it. If TH-cam fails you could always be a math teacher.
10:15 Tyler REALLY tends to overthink. He almost had it right! He fought "multiplie numbers by two, then smush together", but when seeing he was mistaken, instead of thinking "maybe it's the oposite order, smush together and then multiplie by two" he thoght "now it's multipling the first number by twenty and the second by two, then adding". So close...
Why don't you use fractions more often? Seems like that potentially gives you way more information more quickly. Eg when you do 1Y1 = 1, it could be a zillion things. When you do 1.5Y2.5 = 0.6, you can be pretty sure it's division, and even better it may give a frowny face and then you know it might be non-algebraic
Its not that difficult, Tyler just used a weird method. what normal people do is 0 1 6 19 44 85 1 5 13 25 41 4 8 12 16 4 4 4 4 Divide the common 3rd difference by 6 cus math. Wont prove it here but that gives the coefficient of x^3 2x^3/3 = 2/3 16/3 18 128/3 .... original func = 0 1 6 19... diff = -2/3 -13/3 -36/3 -71/3 -11/3 -23/3 -35/3 -12/3 -12/3 Divide the second common difference by 2 to get x squared coefficient -2x^2 -2x^2 = -2 -8 -18 -32 orig f = -2/3 - 13/3 -36/3 -71/3... diff = -4/3 -11/3 -18/3 -25/3... -7/3 -7/3... X coefficient is -7/3 0th term = 1 Full equation = 2x^3/3 -2x^2-7x/3+1 That is what Tyler got but it involves sigmas which is obviously too sigma for an average person like me
4:48 I think that patterns called josephus problem or something, where n prisoners sitting in a circle are labeled 1,2,3, ... n. Prisoner 1 kills prisoner 2, 3 kills 4, then it loops and you have to find the winning seat
In addition to silence, we also edit out overly long explanations until they're more succinct and times I follow a confusing train of logic that leads nowhere. Is this what you expected?
The “phi” function for level 58/61 is actually the answer of the Josephus problem. It is explained really well in an episode by the TH-cam channel numberphile and I highly recommend watching it for anyone who is curious
Wondering if you would be comfortable using a timer for other puzzle games, but I reckon it's a bit distracting for you. It only serve as occasional 'wows' while most of us are satisfied with just your puzzle solving + commentary.
What I meant to say is, timer is not essential and do it if only you want to tylerrr
Handsome and smart what more could we ask for I like seeing you process the information it adds a layer of Emerson
oeis org (apparently I can't post links) is your friend for this. In the case of the first one you had trouble with, it's the solution to the Josephus problem (A006257 on OEIS)
The next one is Tribonacci (add the last 3 instead of last 2, with the first three being 0,1,1), A000073 on OEIS
After that is literally the sequence of numbers whose digits add to 18, A235228 on OEIS (interestingly this one ends at 963, just like the game did)
the next one is the sum of the squares of the first n primes, A024450 on OEIS
then the octahedral numbers (A005900 on OEIS, though interestingly it follows the floor of the sum of the first n^2 square roots until the ninth term, which is 345 there; the difference between the 2 sequences grows slowly) note the octahedral numbers start with 0 at 0, so the nice formula of n(2n^2+1)/3 needs to have the ns replaced by (n-1), which does give the same formula you calculated. There's actually a quick trick if you know the 0th term of a sequence and have calculated the difference sequences, mathologer's video on "Newton's calculus of "what comes next"" does a great job of explaining.
Thanks for the timer, just knowing you weren't instantly getting them makes me feel a little better about myself
Seeing the timer was very enlightening, I've learned that
A) I should not beat myself up for not being able to solve them quickly enough to keep up with the video
B) Tyler spends *way* more time just doing the recording for these than I thought, not including editing, streams, and socials
Thank you for doing your best to always put out daily uploads Tyler! Love your videos and all the cool puzzle games you've introduced me to over the years.
Yeah. Figure a 30 minute video is 90 minutes of recording cut down. And editing takes twice the raw time. That is 4 hours 30 minutes of recording + editing. So 9x the content length to produce.
no fucking idea how he does it, i didnt even know he did daily uploads until i joined the discord server. especially with the quality and length of the content he produces, it's fucking insane.
But he has an editor (as far as I remember) and the longer you work together, the less you have to clarify. Plus you can record several videos in one session.
I think he has multiple editors. Like two or something. Don’t quote me on that tho
This is all fairly expected for me. Honestly I was kinda shocked how little was cut.
Second: Tyler is actually really smart. I am impressed with myself when I can solve it at the same time as him. But there have been times he has come out of nowhere with a massive brain solution, and as such I will never feel bad I didn’t get it along with him because he is genuinely really smart
Honestly the timer seems like a pretty cool idea.
For those that are confused about the wack sequence for problem 58, it’s the Josephus problem. The sequence of 1,1,3,1,3,5,7,1,3,5,7,9… is obtained by doubling the remainder and adding 1, where the remainder is the input minus the largest power of 2 below it. So y=2R+1, where R=x-2^n, where n is the largest power less than x. This function tells you the “winner” of people in a circle who remove the number to their right. In a circle of 5, 1 removes 2, 3 removes 4, 5 removes 1, 3 removes 5, 3 wins. In the function it looks like R=5-2^2=1, so y=1•2+1=3, hence why the input of 5 gave 3. In short, it goes up by 2 each time until you hit a power of 2, where it resets to 1.
th-cam.com/video/uCsD3ZGzMgE/w-d-xo.html
Numberphile explains the sequence origin and solution in better detail there
Thank you, I was looking for someone to say this!
The calculator did a really good job editing this video, nice to see another new member to the team
Wow, Tyler just casually whipped out calculus. The way that sigma popped out of nowhere scared me.
Do you know when he pulled it out (timestamp)?
@@savathunthewitchqueen8299 30:00
Man's a beast
@@savathunthewitchqueen8299 🤨
Thank
I love the timer!
Also, 31:41 has to be the best moment of this series, lmao.
Without a doubt. He got so engrossed in puzzle solving that he made up puzzles just to distract himself from the actual goal.
@@zarnox3071 yo dawg I heard you like puzzles
π
Nothiiiiiiiiiiiiiiing xD
This was amazing xD
@@Xnoob545 I swear I see you everywhere
You wouldnt think a calulator would be this complex, but when you have 2 strange functions and missing numbers while you always have to get 666 is pretty hard (thankfully they gave the player a non cursed calculator)
I mean, the player could bring his own non-cursed calculator
They are also kind of encouraging you to use OEIS which trivializes half of the puzzle. However, that's how real science works, you take whatever you can. I had an university professor who at that time was 70 something and I was politely complaining that his homework exercises were kind of too hard and he answered yes, they are, but you also have Google search. Learned more from that single course than all the others combined that year.
@@FoxSlyme why would we need such a thing? we have tyler
The game also has a calculator if you hold the screen or potentially the tools button
@@johnmielke5840 they literally mentioned that in the original comment when they said "thankfully they gave the player a non cursed calculator"
I love this new editor “calculator.” When I heard Tyler say “it’s 17 again” I knew they would make a joke about the movie.
The description saying "Edited by: calculator" is so fucking funny
Calculator's editing is great, I'd love to see their work on other videos!
"No, I edit them"
-calculator
Tyler is teaching me math in a fun way yet also it is insane how good he is at it
That post it note... back in high school, I would try to do that kind of stuff for fun by hand. I always performed really well in math classes, and I knew when to pay attention, so my teachers were okay with it.
3:46 Josephus problem! Here's my solution that I came up with back when I learned the problem existed
I = input and O = output
(I-2^m)2+1 = O
When m = n-1
When 2^m < I < 2^n
8:50 "... which we all know to be..."
No tyler i have no idea what the hell is going on, still loving it is always satisfying watching tyler solve this things
You kinda figured it out with level 65, but the game allows you to manipulate the result of equations after you've hit enter. It will even allow you to complete the level if you get 666 after using all the functions without clearing. You can see which functions you've used by seeing them light up. Loving the content!
4:49
there's a numberphile video on this one...
the josephus problem!
a way for many soldiers to suicide.
one doesn't want to.
how can that guy survive?
the method:
each soldier kills the one next to him, and the one next to that one kills the next alive one next to them.
repeat until last one standing.
example with 8 soldiers:
1 kills 2
3 kills 4
5 kills 6
7 kills 8
1 kills 3
5 kills 7
1 kills 5
1 is last to surrender and/or suicide.
you can use m1 to save values, and i think it also saves the operations you use to get to that number
4:47 - I believe it's the Josephus Problem. Or, the input is the number of people, the output is the winning spot in the Josephus problem.
The Josephus problem is about a man named Josephus and 40 other soldiers being taken prisoner but I kinda forgot what happened.
So what happens is that all 41 people are stood and ordered in a circle from slots 1 to 41. The first person must start it. Person 1 kills Person 2, Person 3 Kills Person 4, and this goes on - a living person must kill the next living person on his turn. The last person alive will be The goal is to find what number Josephus must be in the circle so that he is the last one alive.
For a problem like this, it stands to reason that every even number slot will be killed off instantly. For a group of 2^n people, the winning slot is always slot 1 (which is why in the calculator, each time Tyler inputs a power of 2, it's always 1). For any group of people of size 2^n + l where l is any positive integer, the winner is always 2l + 1 (you can prove this yourself).
For example, let phi(x) be the function for the josephus problem.
- phi(4) = 1. Proof, 1 kills 2, 3 kills 4, 1 kills 3 so 1 lives.
- phi(12) = phi(2^3 + 4) = 2(4) + 1 = 9. Proof, 1 kills 2, 3 kills 4, 5 kills 6, 7 kills 8, 9 kills 10, 11 kills 12, 1 kills 3, 5 kills 7, 9 kills 11, 1 kills 5, 9 kills 1 so 9 lives.
So for any group of people N where N can be expressed as 2^n + l, the "winning" slot for the Josephus problem is always 2l + 1.
Imagine not solving puzzles with a timer
I could imagine
I could also imagine
I, too, could imagine
I, as well, could imagine.
i already did -_-
I actually recognize the phi sequence on Level 58 (3:30)! It’s the solution to the Josephus problem when starting with n “players.” I recommend looking it up if you like cool math puzzles/sequences!
Tyler accidentally doing calculus in that last level without even realizing it
Calculator the true editor of the channel. Calculator is the channel.
Calculator is the Tyler.
Calculator is Man.
Hey Tyler, not sure if you’ve been watching updates for the games you used to play, but I noticed that Luck Be a Landlord is officially releasing very soon and it just got a final “Landlord” boss.
Love the content as usual can’t wait to see more!
What a coincidence.
At 10:25 I think that it is actually concatenating and then doubling each digit with carry over.
So for 12 fork 5
Concatenate - 1 2 5
Double each digit - 2 4 10
10 carries the 1 to the tens place to become 250
So basically, concatenating and then doubling the result.
Mental Break question @24:00 : I suspect this is what the memory buttons M1 M2 M3 come in handy for - remember that you can use it to tap into burning numbers you can't otherwise access, thereby reducing the cognitive load. =)
Keep in mind, at 14:42 the clock just passed 30 minutes and the the video is 32 minutes long. The editor managed to cut out ~20 minutes already and that seems insane to me
Btw, using the calculus of finite differences would have sped up the last part considerably. It allows you to treat the difference operator very much like the differential operator. And thinking of it that way makes it easy to come up with the formula, since you are simply integrating 4 a few times.
If anyone was wondering, the solution to level 62 is tribonacci numbers. Instead of adding the last 2 numbers, you add the last 3 - so with the starting sequence 1, 1, 1, you get (1+1+1) = 3, then (1+1+3) = 5, then (1+3+5) = 9, then (3+5+9) = 17 etc etc
Honestly I would love to see Tyler explain more stuff like the end of the video. I’m in calculus 3 and this is the first out-of-classroom experience I’ve had that actually uses derivatives in an interesting way
Great vid!
the editing just keeps getting better and better !!!
Seriously, top tier editing.
this was a fun video, I think this format works great for these more "difficult to figure out but easy to execute" puzzle games, where at first glance it looks like you just fly through the game.
"Hey guys, Timer here! And today I'm going to use myself to guage how quick this mere human can calculate the number 666 in this cursed puzzle game!"
Great video as always!! Love the editing on this video and the other recent ones as well!! :D Especially during the intros!
Well, that was extremely fun. Never before have I seen someone so happy to see Fibbonacci
Thanks for walking us through your unnecessary mathematics. It was incredibly engaging.
the editing has been ON POINT lately. Givin some love to the editor today :)
I was also trying to figure out the equation for the last phi's function and I took your sequence (from 29:20) and tried doing a Taylor Expansion assuming the first value was x=0... That wasn't a valid assumption because x=1.
Having good mental arithmetic and being good at maths as a subject are two separate skills. You have both. as someone who is doing physics at uni I followed the last part but was amazed at how you could work out 64 squared in your head
only tyler could make this game interesting enough to make a video on it. I've said this before and I'll say it again, tyler, you are one of the best youtubers out there. not only are you one of the smartest puzzle solving youtubers around but you can make any video entertaining to watch
That was the most beautiful math moment I have witnessed in ages. Reversing a function? I didn't even know that was possible!
Speedrunning Tyler is something I'd never thought I'd see
At level 58, the Phi function was simply all odd numbers before the next power of 2. So 1, then 3 is bigger then 2^1 so it resets, then 1,3, then 5 is bigger then 2^2 so it resets, then 1,3,5,7, then 9 is bigger then 2^3 etc... It is ssociated with a problem where a group of n knight each kill the one to the right of them one after the other, and the last one standing is the value of the sequence.
Just a math tip: “smushing” numbers together is called “concatenation.”
I appreciate the very subtle “17 Again” edit at 16:52
Wow, Tyler has some serious math chops! I'm impressed, and I'm no stranger to scary-looking math. Kudos to you for busting out the big guns for this one, even if it didn't help you in the end.
I love that Tyler used finite differences to figure out it was a cubic polynomial, but at that point wouldn't it be easier to use regression to find the polynomial itself? With known x and y values you just need to solve a 4x4 linear system. Well, that might also take a while if you are doing it with a pen on sticky notes though :/
That was awesome!!! You made math look really fun, it’s been a while since I’ve taken out a piece of paper and tried to calculate a massive function by hand.
Comment for the algorithm lord..
ALSO OH.. GOOD JOB AT EDITING CALCULATOR!!! VERY GOOD EDITING JOB MY FRIEND!!!
So fun fact:
Tribonacci numbers exist (same as Fibonacci numbers except you add together the THREE previous numbers. It starts with 0, 0, 1 (with the first 0 being index 0, and the 1 being index 2), so the rest of the sequence goes 0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, ...)
you fuckin' legend lmao, the end sequence of this video is incredible
goddamnit tyler, that ending absolutely broke me LMAO
also 14 Minesweeper Variants comes out today! I'm excited as fuck to see your videos on the full game, ive been absolutely addicted to minesweeper since these videos came out
always appreciate the editor's notes breaking down what goes on!
4:44 converts the number into binary then moves the leftmost one to the right and converts number back into decimal.
Really loved this episode, the ending was perfect!
You know you love math when you spend 20 minutes finding an equation that doesn't help solve the original problem.
4:47 Yes, there is a more elegant way to describe it. It's called the Josephus Problem (sequence A006257 in the OEIS, if you're interested)
Him standing up with that music is the funniest shit ever
its so fun seeing tyler have fun with math, especially that final reverse engineered equation
Could be wrong here but I’m fairly certain that last equation he made is just an integral of 4 with constants added. Or the derivative of the last equation is 4 if you will.
honestly youre quite good with logical and math puzzles
I frequently try to create specific equations from just a graph. For example, I once made a function where it was the integral of the absolute value of the cosine of x. My goal had just been to make a function where it was a wave that only went up.
So we can finally say that Tyler finishes fast
I love this series so much.. please please let there be more math puzzle games out there
oh hilarious i got a patrick’s parabox ad
Looked up the sequence in that last puzzle in the OEIS and the definition is wildly different than what you came up with. But your solution also works. Just shows how math is weird.
Level 63, the fork option stumped me for ages. I finally stumbled upon the solution you used, but it was blindly throwing numbers at it until 52 came out. When you tested it with lots of 1 fork # I was finally able to see the pattern. This is so fun!
4:46 look up the josephous problem. The sequence is basically the player number that wins in a game of n players in a specific game.
Thanks for playing this game! I'm learning a lot just from watching and I can't wait to watch the next one!
The sequence in Level 58 comes from something I've heard called The Josephus problem, you can look that up if the pattern interests you!
Spoilers for a few functions that Tyler never actually solved:
10:30 The operation here is concatenate first, then double
12:46 The sequence here is similar to the Fibonacci sequence but it always adds the last 3 numbers instead of the last two. It starts with phi(0)=0, phi(1)=0, phi(2)=1 and the missing phi(4)=2.
26:55 phi(n) is the sum of the squares of the first n prime numbers. Check the differences phi(n+1) - phi(n) to see the pattern more easily.
12:46 sequence is called tribonacci for reference.
I wonder if there can be a randomly generated versus mode for this game.
3:30 I believe the function is the solution to the josephus problem, numberphile has a great video explaining the setup and the math behind the pattern.
Love this series, Tyler's math and pattern recognition is amazing so its not boring at all
Tyler missed some patterns because its very hard, and not really needed to solve the puzzle
lvl62: the 'tribonacci series', adding last three terms, 0 1 1 2 4 7 13 24 44 81 149 ...
lvl65: sum of squares of primes 4 4+9 4+9+25 4+9+25+49 ...
lvl66: not enough information lol, wth is that XD
Love the more complicated math you're doing. It's aactually rather impressive that you remembered how to do all that.
Dude really just added a chess clock to the video and somehow he is winning
I really loved the math lesson for a funny punchline
I would have tried to reverse engineer the equation as well. You did it quicker than I would have though.
I think we bullied Tyler into the timer shtick with comments about the editing making him just seem like a genius, which is still possible tbh, but I don’t think anyone was doubting to begin with, just jokes. Cool to know that Tyler’s puzzle ace-manship holds up, but dang I hope it didn’t get to him. Hope not.
Got an ad for Patrick's Parabox while watching the video
Fun fact, the phi function in level 58 is actually the same sequence that solves the Josephus Problem.
Numberphile has a fantastic video on it, but the general gist is N soldiers are stood in a circle, who don't want to be captured, so the first soldier kills the second, third kills fourth, etc, going around killing the next alive soldier until only one is left. The question is what position to stand in to survive.
The answer turns out to be 2L + 1 where L comes from L = N-2^x and L < 2^x (basically, find the largest power of two in the number and subtract it)
The level starting at 3:21 is related to the josephus problem! really cool video by numberphile if you haven’t seen it before
an elegant way to describe the powers of 2 thing is the Josephus problem. it's the one with all the prisoners in a circle killing each other, and to solve it you prove that for n+1 prisoners, the survivor spot moves by 2 places.
this can be proved by saying the prisoner number 1 (who kills first) kills 2, and the 3 becomes the new 1, making it equivalent to the case with n except every index is +2, with the obvious looping if 2n+1 exceeds n.
in other words it's 2n+1 mod 2^(1+floor(log2(n)))
Tyler! I love your vidoes and really enjoy the fact that you upload everyday. I watch every singe one.
Thanks for being awesome!
Like and subscribe peeps!
its incredible to watch him just math shit out while understanding everything but still having absolutly zero idea how he can figure things out and do math in general so fast
oooh yeees!!! KEEP DOING THIS! I always wanted to know this I don't know why I never suggested this. Man that was soo obvious! But that's what I always say, until you think of something for the first time you never thought of it before.
Tyler ,regarding the "powers of two"/"odd numbers" pattern, you might want to check out the Josephus problem. It's used in that, I think (or it's damn similar), and frankly there's some videos/web apps online that are hype in explaining it
That last part killed me that fr like when you do extra credit in math class doesn’t help whatsoever
Well, that was a lot of math for math's sake. Which is sad, but cool that you can actually do it. Even with a degree in mathematics, hell if I could ever know how to get an equation from that sort of sequence. I'd probably never even work out what level of equation it is.
The fork in level 61 concatenates (squishes) the number _before_ multiplying by 2. But the order only matters in some scenarios (paricularly when the second number gains a digit when doubled), which is why Tyler got so confused.
11:05 when Tyler forgets about the possibility of first smosh then *2
Idk why, but the series at 3:52 reminded me of the Josephus problem, where for n number of people where is f(n), the seat that “wins” numberphile (hope I got that name right) did a solid video on it, it’s pretty interesting
You actually make me question my own smarts, I don't think I'd ever be able to do any of that math, let alone in an hour and a half. More respect to ya though, I like how you explain it. If TH-cam fails you could always be a math teacher.
It's absolutely glorious how fast he is with these puzzles
that funny phi thing can be described in if/else as IF x is a power of two, x=1, ELSE x+=2;
10:15 Tyler REALLY tends to overthink. He almost had it right! He fought "multiplie numbers by two, then smush together", but when seeing he was mistaken, instead of thinking "maybe it's the oposite order, smush together and then multiplie by two" he thoght "now it's multipling the first number by twenty and the second by two, then adding". So close...
At 4:20 it’s a series of numbers called the Joseph numbers which is neat
Why don't you use fractions more often? Seems like that potentially gives you way more information more quickly. Eg when you do 1Y1 = 1, it could be a zillion things. When you do 1.5Y2.5 = 0.6, you can be pretty sure it's division, and even better it may give a frowny face and then you know it might be non-algebraic
The only mental break I get is down
I want it to be known that I saw the most witty and well explained advertisement of patrix parabox while watching this
19:12 if 0 can be used then there isn't since 99, 990, 9900, 99000... add up to 18 and there are infinite of them
Its not that difficult, Tyler just used a weird method. what normal people do is
0 1 6 19 44 85
1 5 13 25 41
4 8 12 16
4 4 4 4
Divide the common 3rd difference by 6 cus math. Wont prove it here but that gives the coefficient of x^3
2x^3/3 = 2/3 16/3 18 128/3 ....
original func = 0 1 6 19...
diff = -2/3 -13/3 -36/3 -71/3
-11/3 -23/3 -35/3
-12/3 -12/3
Divide the second common difference by 2 to get x squared coefficient -2x^2
-2x^2 = -2 -8 -18 -32
orig f = -2/3 - 13/3 -36/3 -71/3...
diff = -4/3 -11/3 -18/3 -25/3...
-7/3 -7/3...
X coefficient is -7/3
0th term = 1
Full equation = 2x^3/3 -2x^2-7x/3+1
That is what Tyler got but it involves sigmas which is obviously too sigma for an average person like me
4:48 I think that patterns called josephus problem or something, where n prisoners sitting in a circle are labeled 1,2,3, ... n. Prisoner 1 kills prisoner 2, 3 kills 4, then it loops and you have to find the winning seat