You can always win this game if you go second | An SOS (math olympiad) puzzle
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- Опубліковано 28 жов 2022
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Missed opportunity to replace all the O's with U's
when the math is sus 🤨
Who’s the imposter then?
You are. SUS BOIIIII
NOOO I DON'T WANNA WINN
I DON'T WANNA BE SUUUUUUUUUS
LEL
The difference between this channel and Zach Star Himself is just something else
Throwback to the comedy sketches on this channel back before Zach Star Himself was a thing.
They are both s tier UA-cam channel’s
Yes
fr
Something inside, something inside in my head
Tells me to do, tells me to do things that I can't
Follow me further to the place I wanna go
Light up a fire and let it burn
Through the darkest of my heart
I'll find a place for you to stay even if anger
Hurt and cold turns into pain
I'll burn all emotions, will feel breathless and worthless
Just for you to stay
For you to stay
For you to stay
For you to stay
I've heard your lies a million times over
But your angelic smile washes off my angry side, oh
Honey, you're stone cold, stone cold to me
But I still, but I still can give myself away to you
Through the darkest of my heart
I'll find a place for you to stay even if anger
Hurt and cold turns into pain
I'll burn my emotions, will feel breathless and worthless
Just for you to stay
My eyes are over you
My lips are calling you and I keep running in circles
I need to get a hold of you
Because I wouldn't stand myself without you
So I try and I will...
Through the darkest of my heart
I'll find a place for you to stay even if anger
Hurt and cold...
Through the darkest of my heart
I'll find a place for you to stay even if anger
Hurt and cold turns into pain
I'll burn all emotions, will feel breathless and worthless
Just for you to stay
For you to stay
For you to stay
For you to stay
I like how his skits channel is so chaotic and funny, and this channel is just calm and relaxing to listen to. I love both channels.
they're the same channel
@@DragonSkylander30 Made by the same person maybe, but they do two totally different things for totally different purposes, look again.
This channel also has skits
I didn''t realize it was Zach until he showed up on camera, so I just assumed it was another one of those math curiosity channels for two full minutes
Same
Yes exactly 1:52
Same here
I clicked on the video not knowing it was him and recognized the voice and was like “wait, is this the dude form the skit videos?” And I had to go check his channel
Yeah, and the second I saw him, I thought. Shit this gonna be some dumb shit like actually placing out all 2000 squares on a football field or something.
It needs to be 16 tiles or more because player 2 needs 8 adjacent empty tiles to pull off an S - - S pattern with player 1 being unable to intervene, where when there are 16 tiles, regardless of where or what player 1 plays as their first move; player 2 is guaranteed to have 8 adjacent empty tiles to the left or right of player 1's move in which he can for sure pull off an S - - S pattern.
Player two should only need seven adjacent spaces. When it's his turn, he puts an S in the fourth square from either side. On his second turn, he can put an S on either the first or seventh square from that same side and player one's fate is sealed.
Once player two has made his first move, there's nothing player one can do to stop him because if he plays an O in the first square, P2 can play his S in the seventh, and vice verse. The only way P1 can interfere with building this pattern from either side on his first move is if there's a square no more than seven spaces away from both sides which happens with 13 or fewer total squares.
(Yes, with an odd number of total squares like 13, it's P1 who wants the pattern to be made, but this proves neither play can be stopped from making it if there are 14 or more squares.)
I realized there is a flaw in what I said. The player needs seven adjacent spaces but there also can't be an O already on either side. If there are 14 total spaces, the first player could put an O in one of the middle two spaces and prevent the second player from following this strategy without also setting up an easy win for P1.
@@chitlitlah yes, there has to be 16 squares because if player 1 knows that the trapping pattern is S_ _S, their best first move will always be to bisect the playing field with an O. To block the trap, player 1 has to place an O next to the second S in the pattern, but if the field is big enough there are two possible spaces, so player 1 can't block both. At that point, the winner is determined by whether there are an odd or even number of total spaces in the game.
@@supersonicgamerguru Why not 14? You can mentally split that into two 7 square fields. Player 1 has to place his O into one of them, player 2 can just set up his trap in the other one.
I know that the video says 14 doesn't work at 13:12, I just don't understand why not.
edit: Nevermind, I got it. If player 1 puts an O directly adjacent to that block of 7 squares he could make player 2 add the S when completing the trap and hence giving player 1 the win.
For a player 1 win, the board can be as small as 7 spaces. Player 1 places an S on space 4, then on the next move, whichever of 1 or 7 will create the winning position.
Babe wake up new Zach Star just dropped
Bomb has been planted
@@neoieo5832 Counter terrorists win :trollge:
@@neoieo5832 Legalized Nuclear bombs
swag messiah
There is a concept in chess called Zugzwang and it's at work here as well. I think what's interesting is that player 2 wins because they can basically make a waiting move which forces player 1 to weaken their position
Great analogy
Always funny seeing words from my mother tongue used in really niche areas in English. 😆
Yeah it's like the Zugzwang
Found the answer within 2 minutes using zugzwang concept. This is too easy for math Olympiad puzzle. Is it IMO?
Edit: Ok on seeing the entire video, I can see its USAMO.
Usually these "two players play a game" math problems boil down to the concept of zugzwang. I find them quite easy compared to the other problems they can put there.
This is like one dimensional tic tac toe
no, in tic tac toe you can always tie. here player 2 can always win
@@nomecognome5050 not if its on a 2000 by 2000 grid.
@@theblackphilosopher5958 did you understand the video? player2 can always win games that have an even number of squares greater than 14. No such a thing in tic tac toe
@@nomecognome5050 maybe so, but there are some superficial similarities to tic tac toe
I had a similar thought pattern except 5:12 for 4 squares [S _ _ _] P2 just needs an S in the far column [S _ _ S] and P1 loses no matter what they add next.
Exactly that is what I observed too 👏
At first, I only saw the "Zach Star Himself" channel and it wasn't my cup of tea. I saw this channel and was like "Ugh, Zach Star... but... Math game? I LOVE math games. Let's embrace it and see what happens."
It's awesome and I'm learning and having fun. Love this channel.
My quick answer:
To lose a game, we need a move that "immediately leads to the lost", or: enemy can form SOS and that SOS contains the letter we just placed.
Consider all "safe moves":
Any gap of 3 or larger, we can always put O in the middle
Any gap of 1, we can put O into it.
Any gap of S??O, O??S, O??O, we can put O besides the other O.
There is only one shape that is a "trap":
S??S
We can always play the game safely until the board is full or only left of traps.
Since trap can only have size 2 and the beginning board size is even, the second player can always play safe to not step into a trap.
It's also easy to show that on any large board the second player can always put an S in the middle of nowhere and later put another S on one side to form a trap.
(Enemy can only block one side of it)
Therefore, second player can force the first player step into trap.
If ever playing as the second player, once I create a losing pair, I will speed up the game by continuing to place an S three spaces over from where my last placed S was.
It’s kinda like that box game where whoever makes the box claims it
Something inside, something inside in my head
Tells me to do, tells me to do things that I can't
Follow me further to the place I wanna go
Light up a fire and let it burn
Through the darkest of my heart
I'll find a place for you to stay even if anger
Hurt and cold turns into pain
I'll burn all emotions, will feel breathless and worthless
Just for you to stay
For you to stay
For you to stay
For you to stay
I've heard your lies a million times over
But your angelic smile washes off my angry side, oh
Honey, you're stone cold, stone cold to me
But I still, but I still can give myself away to you
Through the darkest of my heart
I'll find a place for you to stay even if anger
Hurt and cold turns into pain
I'll burn my emotions, will feel breathless and worthless
Just for you to stay
My eyes are over you
My lips are calling you and I keep running in circles
I need to get a hold of you
Because I wouldn't stand myself without you
So I try and I will...
Through the darkest of my heart
I'll find a place for you to stay even if anger
Hurt and cold...
Through the darkest of my heart
I'll find a place for you to stay even if anger
Hurt and cold turns into pain
I'll burn all emotions, will feel breathless and worthless
Just for you to stay
For you to stay
For you to stay
For you to stay
dots n boxes !
@@Rattyrattingratterrattedrat PIGGY
@@SuperPopulated corrrrrrrrrrrrect my fellow friend!
@@Rattyrattingratterrattedrat what??
I love this game, quite a brilliant analyses on your part. Now time to make money off my siblings.
5:15 if player 2 plays an S at the rightmost square, then he wins. That's his winning strategy.
he says "again, assuming optimal play". That is not an optimal play.
@@Caaro99 For player 2 the optimal play IS to play "S" at the rightmost square at that point. Player 1 can't do anything to prevent the win of player 2. Player 1 has to put either an S (which leads to three squares with an S and so to an SSOS or SOSS after player 2's play of an O) or an O (which leads to the same patterns after player 2 puts an S).
@@myrakelvyrm He mean the 1st S by player one is not an optimal play; everyone already knows the optimal play is to put S in the rightmost spot.
if player 1 puts an S in the left/right most slot, its an instant defeat because player 2 only needs to put an S on the opposite side, and no matter what the player 1 does its losing, therefore with 4 squares player 1 will NEVER play S on one of the ends. he can opt to play S in the middle, or O at the end, and it will result in a draw no matter what
if player 1 opts to put O at the ends, O[][][] O[][]S O[]SS (or OO[]S) then player 1 can force a draw
If player 1 opts to put S at the middle, []S[][] OS[][] OSS[] (or OS[]O) then player 1 can also force a draw
because both teams are playing optimally, they will never play a first move that ultimately results in defeat. they will only play moves that results in win, or draw, whichever is better. however with more slots, it is mathematically impossible for player 1 to force a draw, and no matter what strategy they utilize, the game ultimately ends in a loss for player 1
Hey with 4 squares if what you played with S in the first square was "optimal" the second player wins every single time they put an s in the last square then what ever the first player does the second can win
That's what I was thinking
i really appreciated putting the solution onscreen as early as possible while leaving the text large enough to read in fullscreen. video liked
Please don't disregard this channel! I love your skits but you are also a talented and interesting explainer of math and science. You're not a discount 3blue1brown, like honestly there are many things I like about your videos more than 3blue1brown's. Keep this up (if you're passionate).
I like how when illustrating the four cell game, you used as an example the only first move for player 1 that lets player 2 win (just put an s on the opposite end, and no matter what player 1 does player 2 can win by putting the other letter in the final cell).
5:37 If player 1 puts an S in the first slot and player 2 puts an S in the last slot player 2 always wins no matter what player 1's next move is
And he said both players would be playing "optimally", cant believe he let pass such a rookie mistake.
@@ZAYKONN yes, if player one plays optimally they won’t put an s in the first spot
To pull off the double S with two spaces, you need a 7 wide empty area to put the first S in, that way you can place the second one 3 spaces prior or ahead depending on how Player 1 responds. If the number of blocks is too small, Player 1 can place an O near the center and this means that at a minimum you need 7 empty spaces to either side of the O, making the total size 15. However, regardless of which side you construct your double S on, Player 1 will always be able to force you to place the second S on the side closest to the middle, which would place the S right next to their central O, this move would give Player 1 the win so it's not an optimal move, you'd have to abandon the guaranteed strategy. However, if you make the total blocks 1 higher, there's no longer a center, Player 1 now has to play their O on either of the two middle blocks, but will always create 1 side with 7 open blocks and one side with 8 open blocks. Player 2 can start their double S construction on the side with 8 open blocks without the middle O interfering. Add another total block and now the center O creates 8 spaces on either side, and so forth, from this point forward placing an O in the center can not obstruct enough spaces to prevent the creation of the S _ _ S.
It took me a moment to get what you're saying, but you're right. You not only need the seven empty blocks in a row, you need to know that there won't already be an O to either side before you start making the trap.
@@chitlitlah Yeah it wasn't the most concise explanation. After posting it I read Vadrif's comment and they were more succinct with their explanation of the same idea.
While this is true, it's a bit irrelevant. On a size 15 Player 1 would start with an S at least 3 spaces from the edge and aim to create an S _ _ S formation from that. The S _ _ S formation is a win for player 2 when there is an even number of squares. When it's an odd number of squares it will become a win by player 1.
Using 4 squares, the optimal strategy for player one is to either place an O on the edge or either in the middle. Playing an S on the edge gives player 2 the win. Let me explain:
Player 1 SXXX
Player 2 SXXS
Now, no matter what player 1 does, player 2 wins.
I noticed this too. He missed the fact that player two could've guaranteed himself the win on the four-square game, but set up the same pattern on the five-square game and pointed it out.
@@chitlitlah Player 2 can only guarantee a win on the 4 square game if Player 1 does a misplay, which he already said that neither player would misplay. (It is a misplay for player 1 to put an S in the first or last spot of a 4 length board, as that guarantees a loss for player 1.)
a winning strategy means one player can always win no matter what the other does from the beginning of the game, not relying on a misplay. When he said for 4 squares, the game will always end in a tie, he is saying that if no player misplays to the other's advantage, you can't ever form this " S X X S " formation.
@@johncox7169 Then why did he show two misplays?
Your explanation was so much clearer than the written one. Thank you.
Here is why 14 squares or less don't guarantee a win: To make the S _ _ S pattern player2 needs at least 8 empty squares. 7 squares are required to guarantee the pattern can be made either on the left or the right of the 1st S player2 places: "S _ _ S _ _ S", that's because player1 can interfere with his 2nd move on one side, player2 needs to make sure there is still space on the other side. 1 more empty square is needed for the pattern to not be besides the player1 1st move, which might be an O. So if player1 does his first move at the center, it leaves player2 only 7 empty squares on a 14 squares game, which are not enough to guarantee a win.
finally a letter game you can play whilst sitting opposite someone
tic-tac-toe
I love how you didn't find the win for player 2 with 4, decided it was a tie (that is true if player 1 doesn't put a s in a corner) and then found the result by reducing the 5 tile problem into a 4 tile one switching player 1 and 2... But no mention came out
But well, interesting nonetheless
Yea this triggered me
Yep
Pulling off an "s - - s" pattern on a 16-tile game with player 1 playing optimally
1. - - - - - - - o - - - - - - - -
2. - - - - - - - o - - - - s - - -
1. - - - - - - - o - - - - s - - o
2. - - - - - - - o - *s - - s* - - o
This reminds me of the Tower of Hanoi. The problem can be solved if we look at it recursively until we hit the 3-tile base case. It would also help if we used some Graph Theory to analyze all the possible moves and outcomes
i think it's worth mentioning that there is no setup of THREE blanks is a "move and lose" situation. that is, that there are no poisoned squares EXCEPT [S] [ ] [ ] [S] configurations that would allow player 1 to try and swap the polarity back to making player 2 forced to make a losing move. thanks for the video, had fun with the problem
I’m glad you dedicated an entire video to this amazing song!
For 4 squares, if p1 puts an s on the first square, p2 can put an s on the last square and its guaranteed win
not guaranteed, p1 would know this and would put an O on the first or last square
@@NZIsaacNZ im just saying if he puts s on square one.
@@NZIsaacNZ and actually, if p1 puts o on the second spot, its a guaranteed loss, as long as p2 puts an s or an o on the last space
5:20-
S x x S - player 2 copies the S.
SO x S, SS x S, S x O S, S x S S. all player 1 moves lead do player 2 winning.
But this is preventable by placing an O at the start forcing a 3 tile game reversing the order of the players which is still a forced tie.
I just thought the reasoning were a little bit off or I might have understood it wrong...
This whole time I've been watching your smaller channel where you do skits and I never knew you had another channel with over a million subscribers. My mind is Blown!
Nearly 9 years ago I played this game with my friend in middle school. I only know appreciate his smartness. He recently graduated Stanford.
Instead of doing SOS, we circled in dots. We can circle 2 dots or 1 dot. The last one to circle the dots losses or win or something, I forgot. He was an Olympiad winner.
I figured out on the first or second example the s_ _ s template for winning lol, also the example with 5 squares the optimal way would be to put an O in the middle and make a tie
"2000 squares, so a little more than the 10 we see here" yes, just a little more
but in my country, this game is a little bit different than what you show us here... it's not a straight horizontal bunch of squares,... so in my country, in order to win you can create SOS Horizontally, Vertically, and Diagonally... and since it kinda hurt both player's head because they need to pay attention more to each square, the rules changes into "The most player creating SOS is the winner"... so we play it until all the squares are filled.
So .. not the same game, then
Similar but not the same gane
Something inside, something inside in my head
Tells me to do, tells me to do things that I can't
Follow me further to the place I wanna go
Light up a fire and let it burn
Through the darkest of my heart
I'll find a place for you to stay even if anger
Hurt and cold turns into pain
I'll burn all emotions, will feel breathless and worthless
Just for you to stay
For you to stay
For you to stay
For you to stay
I've heard your lies a million times over
But your angelic smile washes off my angry side, oh
Honey, you're stone cold, stone cold to me
But I still, but I still can give myself away to you
Through the darkest of my heart
I'll find a place for you to stay even if anger
Hurt and cold turns into pain
I'll burn my emotions, will feel breathless and worthless
Just for you to stay
My eyes are over you
My lips are calling you and I keep running in circles
I need to get a hold of you
Because I wouldn't stand myself without you
So I try and I will...
Through the darkest of my heart
I'll find a place for you to stay even if anger
Hurt and cold...
Through the darkest of my heart
I'll find a place for you to stay even if anger
Hurt and cold turns into pain
I'll burn all emotions, will feel breathless and worthless
Just for you to stay
For you to stay
For you to stay
For you to stay
Indonesian?
is it a national thing? 💀 i also thought this was how everyone played it
I can’t help but think that a funny punchline is gonna come by everytime he talks because I’m so used to it from his sketch videos
15 is probably the point where you can setup since you need like a 5 Spot difference in to directions to the letter the other Person made right? So that would make like an 11 because 5(for left side) + 5 (for right side) + 1 for the letter and the left over 4 are the places for the setup.
For 4 squares: 1 Plays left s. two Plays right s. Either if an o Or an s are played in either if the both Spots, 2 will win. So if 1 starts with an s on the outside, guaranteed win for 2
i was thinking the same thing, i also made sure that no move can be made to allow the 1 to win or tie in that situation, so starting with an s on either side the number 2 wins for sure, if instead you start with any other move there will be only draws
similar very fun puzzle:
There are 100 bowling pins in a row, numbered 1 through 100. Players A and B will take turns throwing bowling balls at the pins; on their turn they must choose a pin X (which is still standing) and knock down X and its adjacent pins X-1 and X+1. The player who knocks down the last pin wins. Who has the winning strategy?
e.g. if A chooses pin 4 then pins 3, 4, 5 will be knocked down, and then if B chooses pin 6 then pins 6 and 7 will be knocked down (and pin 5 will stay knocked down). Also, note that pin 1 is adjacent only to pin 2, and pin 100 is adjacent only to pin 99.
As player 2 on the four square I would put an s on the other side (S🔲🔲S) and the no matter what player 1 did, I’d win and if player 1 start like (🔲S🔲🔲) I put and S or O (OS🔲🔲) or (SS🔲🔲) -doesn’t matter- and then it would a tie (if optimal play), if it started (🔲O🔲🔲) then Id (🔲O🔲S)(or O) and then it would also tie
Here's an easier game to play that you can always win if you go second. There's one tile and the first person to play anything loses.
Interesting... I remember playing this game, but not on a line, but on a rectangular grid. Where you could spell SOS either horizontally and vertically! Not only that, but when you spelled SOS, you didn't actually won, you scored a point AND was allowed to add an extra letter on the same turn (and if you wrote another SOS, you got to add a third letter, and so on). And so basically the winner was the one that wrote the most SOS in a grid!
the case for 4 letter is a guaranted win for player 2 if player 1 starts with an S in first bracket, that was the short case, cause the trick is for the second player to place the same letter as the first player with a 2 spots gap.
5:13 Player 2 shouldn’t play that O there. The five-player game you show reduces to this with the players switched as soon as you place the second S; if Player 2 had placed an S on the other end they’d win.
It’s a tie if Player 1 plays better, but if Player 1 makes it S _ _ _, they lose.
Came looking for this. :-)
“So a little more then the ten we see here.” Yeah just a few more…
The time you spent in solving this problem is the time given to solve all of the paper. That's how we know genius are out there, even if we spent all of our thought process to a single problem, at the end of the day it's just a problem.
And with that I'm happy 😊 being single.
Man show answer before ad, what a legend
In the one with 4 square there actually is a method IF player 1 places a S on the First TILE and player 2 places a S on the LAST time then player 2 will always win
I realized the trick at 4 squares: playing an s three squares away from another s creates a dead zone that cannot be utilized without giving the other player an assured win. Now the thing is the winner is going to come down to the number of squares. Assuming player 2 IMMEDIATELY creates the death trap, there’s basically a guaranteed winner once all other moves are exhausted. So the winner is whoever makes the last move OUTSIDE the death trap. In odd-square games player 1 wins, in even-square games player 2 wins. Now, player 2 has no obligation to make this losing outcome happen in odd-square games but the point is in the scenario given in the problem, there are 2000 squares, which gives player 2 that edge.
I spent way too long trying to solve the 10 tile case. For game theory questions, I think the strategy to solve a lot of them is to work backwards. If I'm player 2, and there's only one square remaining, then I want to be able to put down an S or O to complete an SOS. That means player 1, on his previous turn, when there were only two tiles left, must have completed either SO_ or S_S or _OS. It couldn't have been _O_ before player 1's move, since he could've played OO_. Likewise, it couldn't have been _S_. Therefore, the two blanks must have been adjacent: X_ _X. Then you run through the cases and only S_ _S actually forces a win for player 2. So player 2 has to force this sequence somewhere, which is easy to do with so much room. Then he just plays on the other tiles to prevent player 1 from winning and eventually, player 1 has to play on S_ _S.
If make a 5/6 box game that wraps around to the start, I wonder if we can consider it as linear tic tac toe
This is better than the channels that say "Google's Interview Question!"
Something inside, something inside in my head
Tells me to do, tells me to do things that I can't
Follow me further to the place I wanna go
Light up a fire and let it burn
Through the darkest of my heart
I'll find a place for you to stay even if anger
Hurt and cold turns into pain
I'll burn all emotions, will feel breathless and worthless
Just for you to stay
For you to stay
For you to stay
For you to stay
I've heard your lies a million times over
But your angelic smile washes off my angry side, oh
Honey, you're stone cold, stone cold to me
But I still, but I still can give myself away to you
Through the darkest of my heart
I'll find a place for you to stay even if anger
Hurt and cold turns into pain
I'll burn my emotions, will feel breathless and worthless
Just for you to stay
My eyes are over you
My lips are calling you and I keep running in circles
I need to get a hold of you
Because I wouldn't stand myself without you
So I try and I will...
Through the darkest of my heart
I'll find a place for you to stay even if anger
Hurt and cold...
Through the darkest of my heart
I'll find a place for you to stay even if anger
Hurt and cold turns into pain
I'll burn all emotions, will feel breathless and worthless
Just for you to stay
For you to stay
For you to stay
For you to stay
For the 4 squares one,
if P1 starts with S///
Then P2 does S//S and he automatically wins
if P1 does SS/S then P2 does SSOS, if P1 does S/SS P2 does SOSS, and if P1 does SO/S P2 just does SOSS and he wins
I am convinced this video is a call for help.
I've been nearly shouting at my phone when you went from the 4 tiles to 5 tiles. All I could think of was S _ _ S, whilst wondering if there was maybe another way, which you were getting at.
I didn’t realize that I found your skits channel from watching this video and getting one of the skits recommended
About 1 year ago, I discovered the 3-corner strategy for Tic-tac-toe.
Honestly, I would just mirror Player 1’s moves and wait for them to create a position where I can win. Since there are an even number of tiles, I’ll never break parity. What I started thinking about when looking at your three-row diagram was “What if you played SOS in a grid?”
If you do that P1 can force a draw by only playing O's
Nobody:
Player 1, 2, and Ronaldo: SOOO-
Fun fact:
If you use a random number of blocks, player 1 is actually slightly more likely to win than lose.
While the minimum even number that player 2 can force a win is 16, the minimum odd number that player 1 can force a win is only 7.
I really like this video!
I remember seeing the first case of such a game in cyberchase "Problem solving in Shangri-La" episode.
please tell me where to get a globe like that! its so cool.
loved the video too lol, reminded me of the Dr. Nim game
Return of the King
5:14 in the 4 square game, player 1 putting an S in the first square would be far from optimal play. All player 2 then have to do is put an S in the last square and they are guaranteed a win, no matter whether player 1 then puts an O or an S in either of the center squares, player 2 gets to spell SOS. Player 1 have to rely on a mistake from p2 or force a tie by puttin an S in one of the center squares, or an O in one of the outer ones.
We’ve already seen this in hand on top of the other game hand 1= 🎉 hand 2= 😮
🎉😮🎉😮 this is just more complicated
I got this by thinking of the other problems I knew where there was a forced win for one player in which we force symmetry. So I supposed that maybe if Player 1 plays an S to the left-most area, we play an S to the right-most. If Player 1 plays an O to the area 3 from the left, we play an O 3 from the right. I found that when Player 1 put an S nine from the left, and we copied, that got the S__S setup and I figured it out from there.
Highly amused when you showed the answer at the end even SHORTER than the first time showing! Yea! Hahahahaha! O:-)
Correct me if I'm wrong, but on 4 tiles, if player 1 puts an S in the 1st or 4th tile, then player 2 can put an S in the opposite, then no matter if player 1 puts an S or an O in tile 2 or 3, player 2 can finish SOS with the appropriate letter. However any other starting moves for 4 tiles would end in a draw, so this starting move wasn't the best demonstration
in the case with 4 boxes, where p1 puts an s on either end, p2 places an s at the other end and forces a win...
This video requires 1.5x speed. Taks so slowly
As long as player 1 doesn’t put an o, just keep putting s until the end. But do it from the other end of your opponent. And if 1 puts an 9, most likely they has SO complete so just add the S
I actually done a math olympiad test b4 and it was tough, they let us bring the sheet back home after results and i still couldnt figure out some questions
Replace O with U for maximal effect
wohw what, Zach has another channel with over twice the subs?
I've only watched Zach Star Himself all these years 🤣
Was really surprised to hear his voice on this lol
the 4 square example does have a winning strategy for player 2 given that player 1 begins in either the first or the last square. For example:
Player 1 puts an s in square 1
Player 2 puts an s in square 4
Now no matter what player 1 does, player 2 will always win. If player 1 puts an s in either square 2 or 3, player 2 can finish off with an o to win the game. Same goes if player 1 puts an o in either square 2 or 3.
So there seems to be a guaranteed win for player 2 IF player 1 starts with an s in either square 1 or 4 right?
I knew you from funny videos, and here you're doing math! :O cool!
I know exactly why did you make this video. When I paused to solve it myself and succeeded I immediately wanted to share my solution with others. Guess it is just natural to feel this way)
Having the game tie when moves run out instead of letting the last mover win makes this just a bit more difficult because it precludes use of surreal numbers directly. I think there's some techniques for games that end in ties, but I haven't gotten to that point in the book yet.
It doesnt increase the difficulty at all because it would just require you to setup more than one (S - blank - blank - S) pattern. Eventually player 1 has to put a letter in between one of the patterns, and because there are more than one, there will always be at least 2 open squares when you win.
5:17 is actually sub optimal play optimal play would be an S completely to the left since that wins for player 2 instead of tying.
This game is usually played on a GRID not a line and goes on until all tiles are filled
This is crazy
Well that is a more elegant than my idea of getting WOPR to brute force the solution.
Oooh this was a fun one
Oh man. I remember filling up pages of a graphing notebook in grade school because we played this a lot
14 is the smallest board where Player 1 cannot stop Player 2 from making the trap with an O on turn 1, but it still feels like Player 2 should be able to force a win...
15 makes sense as a board where Player 2 can set the trap but MUST fall into it at the end - therefore it's best for them to just go for a tie instead.
7 is the smallest board where Player 1 can force a trap without Player 2 being able to do anything to stop them, AND they can win by doing so
Quite simply, Player 1 just needs to put an S on tile 4 of 7
and no matter what tile Player 1 puts an O on a 14 tile game, Player 2 always has 7 tiles to work with for making the trap, plus an extra 6 spares to wait out the game with - Effectively, a 13 tile with Player 2 as Player 1.
Before 7 tiles, it's luck (or always a tie). Before 14 tiles, it toggles between Luck and Player 1, and after 13 tiles, it toggles between Player 1 and Player 2 always having a win, based on which one has the odd board first.
I don't have any experimentative evidence to show here, I just thought about the minimum tiles to create a trap with 100% certainty, and the leftover tiles before SOMEONE must play into the trap.
5:39 with 4 squares player 1 puts a S in the first spot. I, the second player puts a S on the forth spot, and win always.
The 4 squares is only a tie when you start putting an o on the first spot.
Okay, I figured out why 14 spaces doesn't guarantee a P2 win.
Move 1:
P1 plays an O on either space 7 or 8, directly blocking P2 from using that side (1-7 or 8-14) to set up their S _ _ S trap (since 7 spaces are needed). We'll use space 7 for this example, but this and all other moves could be mirrored and it still holds true.
_ _ _ _ _ _ O _ _ _ _ _ _ _
Move 2: P2 plays an S four spaces from the other end (space 11) since that's the only way remaining for P2 to make S _ _ S without P1 directly interfering. If P2 puts it in 1-6, P1 can block with an O two or three spaces away toward the more empty area. If P2 plays S in 8-10 or 12-14, P1 can play an O using the same strategy as on the other side. If P2 plays an S in 11, then whichever way P1 goes, P2 can play another S in 8 or 14 to make S _ _ S... In theory, at least. In practice, not so much...
_ _ _ _ _ _ O _ _ _ s _ _ _
Move 3: P1 can now break the S _ _ S strategy by playing an O in 14.
_ _ _ _ _ _ O _ _ _ s _ _ O
Move 4: P2 can't use the S _ _ S strategy any more. If P2 puts an S in 8 like the strategy calls for, P1 can simply end the game with an SOS in 6-8. Putting S in any of the spots 1-6 is still just as blockable as in Move 2. A different strategy must now be used.
Any more than 14 spaces makes one half of the field unblockable for P1. P2 can always just put an S four spaces from the other end of where P1 initially played, and P1 can't block a successful S placement either in that very last spot, or in the spot three more inward, on P2's next move.
Basically, the strategy boils down to figuring out whether you always move with an odd or even number of spaces open to you, and then trying to either force S _ _ S to be created (odd) or keep it from being created (even). If there are more than 14 spaces on the board to start and you're even, you're screwed.
in the 4 tile case, P2 wins if P1 puts an S in either end.
just need to put an S on the other end and now no matter what P1 does, P2 wins
If there are an even number of squares, can't player two just mirror what player one does on the left or right side so that it will always to player one's turn to make a losing move?
In the 4 squares example, if player 1 plays an S on the first tile it guarantees a win for player 2 playing an S on the last tile : S, , , S
So while player 1 can force a tie by playing an O, he can't do so with an S on the first or last tile, player one also can't force a win
Something inside, something inside in my head
Tells me to do, tells me to do things that I can't
Follow me further to the place I wanna go
Light up a fire and let it burn
Through the darkest of my heart
I'll find a place for you to stay even if anger
Hurt and cold turns into pain
I'll burn all emotions, will feel breathless and worthless
Just for you to stay
For you to stay
For you to stay
For you to stay
I've heard your lies a million times over
But your angelic smile washes off my angry side, oh
Honey, you're stone cold, stone cold to me
But I still, but I still can give myself away to you
Through the darkest of my heart
I'll find a place for you to stay even if anger
Hurt and cold turns into pain
I'll burn my emotions, will feel breathless and worthless
Just for you to stay
My eyes are over you
My lips are calling you and I keep running in circles
I need to get a hold of you
Because I wouldn't stand myself without you
So I try and I will...
Through the darkest of my heart
I'll find a place for you to stay even if anger
Hurt and cold...
Through the darkest of my heart
I'll find a place for you to stay even if anger
Hurt and cold turns into pain
I'll burn all emotions, will feel breathless and worthless
Just for you to stay
For you to stay
For you to stay
For you to stay
We used to play this in a graphing paper when I was in elementary but we use X and O
I remember playing this game during 2nd grade middle school, this was a popular game before but after I got transfered school I didn't play it anymore because there are many different popular games before
We were playing with a graphing paper and the one who has the most placed SOS wins
Had to watch the video again because I was distracted by the spinning globe
You also have to show that you can always play a move that doesn't give the opponent a win on his next move. Placing an O next to an O never gives a win, and placing an S next to an S never gives a win unless you are in the SBBS case, which is always avoidable due to parity.
If a game with n cells is lost by P1, the latter can win the "n+1-game" by placing an O in the leftmost or rightmost cell, making P2 the first player of the remaining n-game.
If a game with n cells is won by P1 with the right first moves, and drawn or lost with the others, P2 can prevent their defeat by picking one of the losing or drawing options for P1. So there can't be any non-winning first move for P1. Even if P1 places an O in the leftmost or rightmost cell, they'll win, which means P2 wins the n-1-game.
We can figure out that an n-game and an n+1 game can't both be won or lost by P1. All odd numbers of cells lead to P1 winning, and all even numbers of cells lead to their defeat, because P1 wins a 7-cell game, so P1 loses a 2000-cell game.
when it cut to the face cam i was just staring at the floating globe until i saw "get the floating globe" in the corner, i laughed
Interesting analysis. Reminds me of playing connect 4, where this idea comes into play intuitively.