I have been looking at this for a while now and I am not convinced that it isn't possible to force mate in under 24 moves by playing 1.d5. I would like to see a thorough explanation with a large variety of lines shown as to how Black can defend against this.
Jerry's brief explanation of Black's knight checking from d2 and freeing the Black king just doesn't offer enough to convince me that this can delay White's promoted queen for so many moves.
@22hoooly If he doesn't do Bxd2, and moves to let's say Kc3, Black forks with Nf3+. If he does instead Kc5, black has a number of options that very well cud win, or atleast delay the game PAST the 24move limit that was predetermined by the problem. Black could start pushing the h pawn to queen, and if white mimics, black still gets away from the Qa8+(or Qa6+) with Kb3, and then he keeps running. And if the checks ever fade, black counters with Qd5+. Now white is on the run.
@TheObamaNigger I wrote a software that calculates the possibilities until move 17 by white. I did so by reusing some code that I already had written for some other type of chess/maths problem. That software was designed to set up a chess position, make a fixed number of legal moves and search for appropriate results. As I extended this computer program, it's not so neat or efficient and I prefer not to show it. But I'll give some details.
The main task is to count all the ways to go from the initial position to the one after 17. Bxh1 - and this what my software does.
I set up the start position as wBa8, bPh4, bPh5, bPh6, bPh7 and the final position as wBh1, bPh3 (keep in mind: movements are restricted). The task is to make 33 (half-)moves and check whether the final position is reached. I did so by making use of the backtracking algorithm. A recursive method does the job.
The number of paths thru the network of allowed moves is 12376, so this equals the number of mathematical speaking "legal permutations of pawn moves". After all those pawn moves we get 8 (correct? Someone should prove that) different variations (permutations of legal moves) to get the king mated in 24 (and not less!). So the overall number is 12376*8 = 99008 different (!) forcing mates in 24 moves.
I found the solution to your mathematical problem:
The key to the number of sequences lies in the number of possible pawn moves to get all pawns except the 7.rank pawn down to the first rank, where they will be eaten up by the bishop. The legal number of pawn positions is 56. I did wrote a little java program which counted the number of variations by expressing the problem as a network of legal moves that lead to the 7th rank pawn going down to rank 2. to be continued... see next post
Black bishop to g2 loses as described earlier - in a slightly different way - White bishop captures on g2, and after the the Black pawn captures White bishop, White plays Bb4 followed by b3# no matter what Black does. I think Jerry will agree with this.
cant you win in two moves if you move your pawn at 2b to 3b to put the black king in check. the only spot the king can move to is 3a. then move your bishop at 1e to 4b for checkmate. right?
man as much as I appreciate the complexity of this position it is SO theoretical, never, in the thousands of games that I have played have I seen quadrupled pawns, and I find it difficult to conceive a realistic situation where such a position could arise... irregardless, the commentary was great and as a mental exercise its wonderful.
@elgrau1 I was instantly able to recognize you as the tool in this situation. You even stopped replying to the guy to try and feel better about yourself getting the "final word". roflmao, this whole 10 year old culture on youtube is very interesting as of late, tons of people with out any ability to hold a conversation, discussion or argument. Just putting in personal opinion and not backing up anything with fact or intellectual point of view.
@elgrau1 Roflmao, thanks for proving my point guy. It's funny how you can just set up a moron such as yourself to do tricks and you just beg on command, thank you for making my day.
I see something similar to a monopoly puzzle, I'm guessing that it's the derivative of sections: akin to a piecewise function, how ever I can solve this
I think for the problem to be well defined, it's how many game paths lead to check mate by white in 24 moves. If a move by white creates a way for black to prolong the game further, it's not best play. If a move by black creates a way for white to shorten the game, it's not best play. I guess part of the proof needs to be that 24 moves is min-max.
this is a simple zugzawng problem. The odd looking position looks impossible to figure out but an experienced chess player like myself would quickly notice that almost all of the pieces on both sides cannot move. I have experienced zugzawng in my games but never to 24 moves deep.
@elgrau1 why because i'm intelligent enough to solve a simple pattern recognition problem? must suck to be such a retard like yourself, jealous of other ability to use cognitive thinking. Hey if this is too hard try checkers.
@elgrau1 lol you mad bro? all i said was that i was able to solve it quickly. As a matter of fact, i instantly recognized the theme. Sorry that makes you feel inferior? i don't know what else to tell you.
also, does promoting to different pieces constitute a variation? (they are eaten right away)
If so, can you promote to a pawn? how about an opponents piece? (I'm going to assume "no" on all 3 counts, but I'd really like ChessNetwork, or someone versed in the stuff to say definitively)
@MrWorldking That frees up the White dark square bishop after the exchange of light squared bishops, as stated in the video @3:28. White can therefore place his remaining bishop on b4 with pawn to b3 #mate to follow
um....if you assume best moves; White playes, bh1, black plays h3, white plays ba8, but now black can play bg2. White is now screwed. and there are no solutions.
@geheirnwaeshen after black plays Bg2 white plays Bxg2 and after black plays Hxg2 white plays Bb4 and regardless of which pawn black promotes (or what black does for that matter) white plays B3# checkmate!
I have already pointed out how to master the complexity of this problem. The first part can be calculated by brute force using an appropriate computer program. The second part requires not much of thought. The third part is easily done by enumerating all possibilites. Unfortunately, I do not get a feedback, even by the maker of the video. Instead my post is marked as spam. That's too hilarious! Thx for all this ignorance.
Of cource most of moves variations would end game much faster, but chess positon also can not be charactersed using only one floating point operation (FLOP) unlike I assumed earlier. Nevertheless todays top chess computer can solve about (optimisticly estimated) about 10^10 positions in second, which isnt helping us.
Very interesting problem, but computer cant calculate another checkmate variation, because of amazingly large number of variations. If we assume that every turn you have about 10 possible moves then we have 10^(24+23) sometimes we have more than 10 possible moves, sometimes less. If we assume, that we have top 500 supercomputers with combined computing strength of 3.24*10^16 flops, it would take roughtly 3*10^31 second, which is about 10^22 years.
I solved it. The position after move 17 by white can be reached via 113,536 ways. I wrote a computer program to do this. Moves 17 (of black) to 21 (of white) are almost unique, just on move 19, two promotions are possible, Q or B. Finally, there are 56 possibilities for moves 21 (of black) to 24 (by white). So, we get 113,536*2*56 = 12,716,032.
What I don't understand is why you say there are so many variations. I mean: you say "assuming best play," that does not leave many variation from the solution you already gave. I can't see any variation before black move 21. What am I missing?
@TyYann Black can decided what order to move the pawns on the side in (not necessarily one against the other) and what order to sac the knights in, as well as white have the pawn option for one brief turn which the author didn't mention. The bishop and pawn add multiple angles of checkmate which makes the number of combinations of moves and permutations ridiculous.
black can win the game. when black has all of it's pawns at h2, h3, h4, h5, the white bishop is at h1 and it's blacks turn to move. black can put his bishop infront of white's bishop blocking it off (on the g2 square), either forcing white to take it or letting white take his bishop. either way, the black pawns will reach the end and create 4 queens (at most). so white loses
Lol, anyone found the solution yet? I can only get as far as multiplying the number of possible combinations of the first 18 moves with the last 6, since it's impossible to move a black piece before all the pawns, except one are gone.
Both parts of the problem are very difficult. There could be millions of possible variations.
@jwelihinda because then you wouldn't have the discovered attack from the bishop when queening. meaning you can move the bishop to b4, then pawn b3 mate.
If it has to start with the best move, there is only one best move and that best move has to end it in 24 moves, therefore there is only one solution. -Luis Figueroa, P.R.
@mashka888 WRONG!!!!!! After bishop to b4 black pushes pawn to e1 causing discovered check. Whites only move is then king to c5. Black then plays queen to b4 taking the bishop and causing checkmate.
@mashka888 This is entirely wrong, black advances the pawn and promotes with discovered check from the bishop on f1. He even says as much in the video
at 4:24 why doesnt black just move his bishop to g2 trapping the white bishop? White would then have to take blacks bishop and then black would just recapture with his pawn from h3
@tatomuck18 Was the exact same thing I saw. Answer to his last question, since you have to assume best moves is zero, white never wins this game unless black is an idiot.
I have a solution to your "unsolved' problem. The key words in the question are "assuming best play" which you did NOT demonstrate in your given solution to the first problem. Assuming best play Black will always win! Afterblack has a pawn on h3 and the white bishop is on h1 black need only play bishop to g2, traping the white bishop. Play continues h1xg2 , h3xg2 and and black will promote to a queen next move. Should white not take the black bishop then g2xh1 and black gets a queen in 2 moves
@craigberry007 two moves is too late. After the exchange of bishops black no longer has the threat of discovered check with the bishop and white plays Bb4. Black Queens but white then delivers checkmate with b3. I saw the same thing, but as you can see white has a reply.
@craigberry007 promoting a queen does not equal a win. i have gone over this position on my comp several times. if the if Bb2 white will still win by force
im not great at chess.. but @5:10 why cant f1-g2? its protected by the pawn on h3 and it forces white bishop to take it but then pawn can keep moving.. can anyone explain why this is bad for black?
Based on the Everett Theorem me and me colegues using the prolonging technique of pawns discovered gravity in 24 moves so we concluded that the solution is definetly a number! How cool is that! :p
Nice video - Who the author of the problem?! (sorry if i'm failing to visualize, but a published Chess Problem should be accompanied by:) (a) Author (s) (b) Place and Date of first publication (c) The Prize or other nomination awarded (eventually) Thanks for the attention
Thus, so far: 2^10 x 3^2 h pawn combinations. Now the final BLACK's 18-23 Moves: 18..Nb7, 19..=Last 'h'pawn promotion, 20..Bg2, 21..Nf3, 23..'e' pawn promotion ALL forceful. Move (22...Nf3 or Ne4) = 2 choices
So, Final Solution: 2^ 10 x 3^2 (h pawn combinations) x 512 promotion permutations x 2 = 2^20 x 3 ^2 = 1048576 x 9 = #9437184 different mates in 24. Hope I've helped!!
@Neueregel That seemed to helped, but what are the 5 forced moves, cause i couldn't follow? Has that to be when the bishop occupies h1 and therefor makes h1/QRBN impossible?
Is a bit hard write all number of moves sequences out i guess :(. Wonder if there are more studies like this with that much combinations that leeds to the fasted checkmate. Nice problem.
@serrie85 Hey there. No, by 'forceful' moves I meant only forceful 'pawn' moves. Not knight. That means, one choice of 1 pawn moving forward each time. When these first 17-18 black's 'h' pawn moves finish (i don't remember the number exactly) , ONLY THEN the knight start to move. Remember : The goal is to prolong the Checkmate as soon as possible. Cheers.
1-17 Moves: All are 'h' pawn moves, since anything else leads to a quicker mate. Now move 1 is a forceful move 1..h3 . Also there are 4 other forceful h moves, when we have to avoid a row of congested pawns at g2,g3,g4 etc. So 5 forceful moves. The remaining 12 moves are always choices of 2 different pawn moves (10 times), except the cases of triplette formations of h7-h5-h3 and h6-h4-h2 where we have 3 movement choices(2 times).
BLACK's MOVES Pawn promotion permutations= 1024 (we have 5 different pawns with exponent to 4 different pieces promotions for each pawn}) So 4^5=1024. However, last 'h' pawn, on move 19 cannot be Rook or knight because it cannot control the diagonal. So 4^4x2=2^9=512 different permutations.
WHITE's MOVES: 19 forced oscillations between a8-h1(with capturing or not) PLUS the 5 forced moves 19. Bxb7, 21.Bxg2, 22.Bb4 .(23 Bxf3 or Bxe4), and 24. b3## White's Move 23 forcefully depend on black's 22nd move respectively. So White has no options, is just reacting and the problem is reduced to just the combinations of BLACK's 23 moves
it is indeed possible, tho only in a theoretical level. all the captured white pieces would have to be captured at the apropriate squares by the corresponding black pawns - except for one. the black pawns have committed 9 captures to get to this position and theres 10 white pieces missing.
does the total number of combinations also include black intentionally letting white promote a pawn to queen then he dinks around for like 15 moves to mate? cause if so that would be unimaginable number
as the moves a pretty much set on what black and white must do the main factor that increases the variations is the location the peices moved to get captured ex... knight to e4 and knight to f3 so if you find all possible moves for each peice then multiply them together you get your answer?
Ah hah! Found it. Not the answer, your video, lol. Simple enough title, I was afraid it was going to be a realization during one of your blitz games "Oh, and this current setup has the most possible outcomes," thankfully, wasn't the case. I wonder if the problem has a name?
will the black should not move his pawn from H3 to H4 he should move the other pawn from H5 to H4 and here is the possibelties after the H5 to H4:
1- E1 to H4 so the black king will pass to A5
or
2- A8 to H1 so the black will move F1 to G2, then the white E1 to B4, so the black G2 to D5 by that black will force the white king to move for C3 after that the black king will pass to B5
Are we also to assume that the white's "best move" is the bishop oscillating back and forth? You didn't specify white's "best move", you just gave your opinion. It's not really a fair question because "best move" is subjective.
I didn't give my opinion on the bishop oscillating. A solution was given to the mate in 24 which implies bests move since the goal is to mate as soon as possible.
1, because if we are assuming best play, only one should be the answer as the rest would be positionally weaker. But since I know you didn't really mean "best play" literally... i will come back with another answer..
@JustAnotherPers0n oh and this isnt a very complicated problem, just a little annoying to solve.. it simply involves a few combinations and permutations, have to account for the number of types of in between moves.. for example the knight moves in between and the pawn moves in between, so on.. basically something like X*Y*Z*T each letter representing the number of inbtwn moves for each type the only problem is.. the inbtwn moves can be interlaced with different types, just an annoying problem :)
@JustAnotherPers0n sorry after taking a look at it again the different types of X number of moves cant be interlaced, it is pretty constricted so, but the different way to lose knights can be interlaced.. so yes disregard the last sentence.. soo X numbers of pawn*Y number of valid "best play" knight 1*2 *Z prolonging moves(bishop & others i havent taken much time to read into this position)
This has been flagged as spam show
who gives a shit my question is how do u get 4 ponds lined up in a row?
SolidSoul40373 2 days ago
y r blacks pawns quadroopled?
Mdaske 3 weeks ago
haha genius
cwxzeng 1 month ago
its 416
Aseninejoe 2 months ago
I have been looking at this for a while now and I am not convinced that it isn't possible to force mate in under 24 moves by playing 1.d5. I would like to see a thorough explanation with a large variety of lines shown as to how Black can defend against this.
Jerry's brief explanation of Black's knight checking from d2 and freeing the Black king just doesn't offer enough to convince me that this can delay White's promoted queen for so many moves.
1.d5 Ne4 2.Bc6+ Nxc6 3.dxc6 etc.
22hoooly 2 months ago
@22hoooly 1.d5 Ne4 2.Bc6+ Nxc6 3.dxc6 ...Nd2+!
If Bxd2, e1+ (discovered attack by bishop AND new queen)
UGB6WX 1 month ago
@22hoooly If he doesn't do Bxd2, and moves to let's say Kc3, Black forks with Nf3+. If he does instead Kc5, black has a number of options that very well cud win, or atleast delay the game PAST the 24move limit that was predetermined by the problem. Black could start pushing the h pawn to queen, and if white mimics, black still gets away from the Qa8+(or Qa6+) with Kb3, and then he keeps running. And if the checks ever fade, black counters with Qd5+. Now white is on the run.
UGB6WX 1 month ago
Comment removed
kakashi76767 2 months ago
Y knot Bg2?
geekintheperimeter 2 months ago
Well, as to solving the problem, lol... I used to study this type of math and know how challenging that can be. Good luck to those who attempt indeed!
As to me, I get perfectly happy after drinking a couple bottles of beer!
NewVahan2011 3 months ago
@TheObamaNigger I wrote a software that calculates the possibilities until move 17 by white. I did so by reusing some code that I already had written for some other type of chess/maths problem. That software was designed to set up a chess position, make a fixed number of legal moves and search for appropriate results. As I extended this computer program, it's not so neat or efficient and I prefer not to show it. But I'll give some details.
AnotherProblemist 3 months ago
The main task is to count all the ways to go from the initial position to the one after 17. Bxh1 - and this what my software does.
I set up the start position as wBa8, bPh4, bPh5, bPh6, bPh7 and the final position as wBh1, bPh3 (keep in mind: movements are restricted). The task is to make 33 (half-)moves and check whether the final position is reached. I did so by making use of the backtracking algorithm. A recursive method does the job.
AnotherProblemist 3 months ago
lmao... why is there so many h pawns...?
0xan4xan0 4 months ago
@themafia306 bb4 and mate in 1 :)
AsusMu 6 months ago
@AsusMu . If Bb4 the pawn promothes, check, king moves and Queen takes b4
jitoski77 4 months ago
@jitoski77 he ws answering the top comment
rwarnicke 4 months ago
Comment removed
moonblink 6 months ago
haha
to figure out is almost impossible unless you had a board.
I think grandmasters hold only 10 moves ahead
Franchan10 7 months ago
dot org slash view slash code colon 1d70
erbse1178 7 months ago
codeviewer
erbse1178 7 months ago
You may please check if I am right, the code is here.
erbse1178 7 months ago
The number of paths thru the network of allowed moves is 12376, so this equals the number of mathematical speaking "legal permutations of pawn moves". After all those pawn moves we get 8 (correct? Someone should prove that) different variations (permutations of legal moves) to get the king mated in 24 (and not less!). So the overall number is 12376*8 = 99008 different (!) forcing mates in 24 moves.
Thank you
erbse1178 7 months ago 2
I found the solution to your mathematical problem:
The key to the number of sequences lies in the number of possible pawn moves to get all pawns except the 7.rank pawn down to the first rank, where they will be eaten up by the bishop. The legal number of pawn positions is 56. I did wrote a little java program which counted the number of variations by expressing the problem as a network of legal moves that lead to the 7th rank pawn going down to rank 2. to be continued... see next post
erbse1178 7 months ago
Horse in g7 after two pawns move forward, could may open the lock ;)
mancusofilippo 7 months ago
so how did he solve it
MilitaryMan006 8 months ago
What about black bishop to g2?
themafia306 8 months ago 7
Comment removed
moonblink 6 months ago
@themafia306 if bishop to g2 you take it and after hxg2 bishop b4 and no matter what b3 will mate
rwarnicke 4 months ago
@themafia306
Black bishop to g2 loses as described earlier - in a slightly different way - White bishop captures on g2, and after the the Black pawn captures White bishop, White plays Bb4 followed by b3# no matter what Black does. I think Jerry will agree with this.
NewVahan2011 3 months ago
@themafia306 it just gets taken by the white bishop??
89Koalito 2 months ago
Where is the solution posted?
SuperMyfamily01 9 months ago
@QuackWackWack hehe good point, my bad!
turtleguy910456686 10 months ago
surely there can only be one best play solution?
Turkey892 10 months ago
cant you win in two moves if you move your pawn at 2b to 3b to put the black king in check. the only spot the king can move to is 3a. then move your bishop at 1e to 4b for checkmate. right?
turtleguy910456686 10 months ago
@turtleguy910456686 King can go to a2
LakerNarutosasuke32 10 months ago
man as much as I appreciate the complexity of this position it is SO theoretical, never, in the thousands of games that I have played have I seen quadrupled pawns, and I find it difficult to conceive a realistic situation where such a position could arise... irregardless, the commentary was great and as a mental exercise its wonderful.
victav 10 months ago
Comment removed
e4mikey 11 months ago
i was able to instantly recognize that you are a tool. looks like we both have a gift.
elgrau1 1 year ago
@elgrau1 I was instantly able to recognize you as the tool in this situation. You even stopped replying to the guy to try and feel better about yourself getting the "final word". roflmao, this whole 10 year old culture on youtube is very interesting as of late, tons of people with out any ability to hold a conversation, discussion or argument. Just putting in personal opinion and not backing up anything with fact or intellectual point of view.
Cawby 9 months ago
@Cawby Well aren't you a snarky little prick? You're trolling so hard, you comment on a thread that's over 3 months old. Get a life.
elgrau1 9 months ago
@elgrau1 Roflmao, thanks for proving my point guy. It's funny how you can just set up a moron such as yourself to do tricks and you just beg on command, thank you for making my day.
Cawby 9 months ago
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@Cawby How is what you are doing any different?
elgrau1 9 months ago
@5.17 1. ...h4 2. Bh1 Bg2
IdiosyncraticChild 1 year ago
@IdiosyncraticChild the black bishop can't move away from the f1 square, because then white can play Bb4, and checkmate is inevitable
Kristaps99 1 year ago
I see something similar to a monopoly puzzle, I'm guessing that it's the derivative of sections: akin to a piecewise function, how ever I can solve this
PriestRSC 1 year ago
"Best play"?
I think for the problem to be well defined, it's how many game paths lead to check mate by white in 24 moves. If a move by white creates a way for black to prolong the game further, it's not best play. If a move by black creates a way for white to shorten the game, it's not best play. I guess part of the proof needs to be that 24 moves is min-max.
carlosjhr64 1 year ago
this is a simple zugzawng problem. The odd looking position looks impossible to figure out but an experienced chess player like myself would quickly notice that almost all of the pieces on both sides cannot move. I have experienced zugzawng in my games but never to 24 moves deep.
laputadetumadre11 1 year ago
@laputadetumadre11 u sound like an unbelieveable tool
elgrau1 1 year ago
@elgrau1 why because i'm intelligent enough to solve a simple pattern recognition problem? must suck to be such a retard like yourself, jealous of other ability to use cognitive thinking. Hey if this is too hard try checkers.
laputadetumadre11 1 year ago
@laputadetumadre11 no, because you sound like a pompous douche bag
elgrau1 1 year ago
@elgrau1 lol you mad bro? all i said was that i was able to solve it quickly. As a matter of fact, i instantly recognized the theme. Sorry that makes you feel inferior? i don't know what else to tell you.
laputadetumadre11 1 year ago
the answer is 2
massussuss 1 year ago
the first puzzle was easy :P yeah i solved it in 24 ! :D i thought that it had to be the most weird puzzle ive ever seen :P
the second puzzle ... damn , it is hard , im gonna have to think about it !
misterkefir 1 year ago
also, does promoting to different pieces constitute a variation? (they are eaten right away)
If so, can you promote to a pawn? how about an opponents piece? (I'm going to assume "no" on all 3 counts, but I'd really like ChessNetwork, or someone versed in the stuff to say definitively)
a1024s 1 year ago
However, I have a question of my own: What constitutes "best play"?
a1024s 1 year ago
so whats wrong to black bishop to g7 and forcing the exchange of the white bishop
MrWorldking 1 year ago
@MrWorldking That frees up the White dark square bishop after the exchange of light squared bishops, as stated in the video @3:28. White can therefore place his remaining bishop on b4 with pawn to b3 #mate to follow
BorderlineHC 1 year ago
According to Rybka Engine. white should play d5, if Ne4, then Bc6+ NxB pxN, white pawn is unstoppable
albertolmolina 1 year ago
You could of sacrificed a black night, to make a pawn queen then busted out of the situation.
fiieeldy 1 year ago
um....if you assume best moves; White playes, bh1, black plays h3, white plays ba8, but now black can play bg2. White is now screwed. and there are no solutions.
geheirnwaeshen 1 year ago
@geheirnwaeshen after black plays Bg2 white plays Bxg2 and after black plays Hxg2 white plays Bb4 and regardless of which pawn black promotes (or what black does for that matter) white plays B3# checkmate!
TheMikey00004 1 year ago
I have already pointed out how to master the complexity of this problem. The first part can be calculated by brute force using an appropriate computer program. The second part requires not much of thought. The third part is easily done by enumerating all possibilites. Unfortunately, I do not get a feedback, even by the maker of the video. Instead my post is marked as spam. That's too hilarious! Thx for all this ignorance.
AnotherProblemist 1 year ago 2
@AnotherProblemist You are correct, However laypeople think you are shit-talking. You can shut them up by posting your solution though.
a1024s 1 year ago 2
Of cource most of moves variations would end game much faster, but chess positon also can not be charactersed using only one floating point operation (FLOP) unlike I assumed earlier. Nevertheless todays top chess computer can solve about (optimisticly estimated) about 10^10 positions in second, which isnt helping us.
Alkku 1 year ago
Very interesting problem, but computer cant calculate another checkmate variation, because of amazingly large number of variations. If we assume that every turn you have about 10 possible moves then we have 10^(24+23) sometimes we have more than 10 possible moves, sometimes less. If we assume, that we have top 500 supercomputers with combined computing strength of 3.24*10^16 flops, it would take roughtly 3*10^31 second, which is about 10^22 years.
Alkku 1 year ago
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@ChessNetwork
I solved it. The position after move 17 by white can be reached via 113,536 ways. I wrote a computer program to do this. Moves 17 (of black) to 21 (of white) are almost unique, just on move 19, two promotions are possible, Q or B. Finally, there are 56 possibilities for moves 21 (of black) to 24 (by white). So, we get 113,536*2*56 = 12,716,032.
AnotherProblemist 1 year ago 5
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best play is subjective so it cannot be proven
JustinKennith 1 year ago
Use a pc....
V10RRV 1 year ago
After depth 29 stockfish was able to solve the problem :-P
skreyer 1 year ago
easy, 1... X 1423638392380293720374
GHalfa 1 year ago
@GHalfa Easy, it's easy without using calculator?
alinusD 1 year ago
The pawn can move forward for white - if the bishop is on the h1 square guarding against the g5 knight.
HiImBobBum 1 year ago
A tablebase will show it. How far into the future we will have to go to get a tablebase of that size, i dont know.
wikipediaXXorg/wiki/Endgame_tablebase
stegtenudlar 1 year ago
easy, 14,244,875.86
momez86 1 year ago
What type of credit and how much credit?I'm just joking.But I still want to find out.
Penguincw2 1 year ago
google- get those fucking adverts off
vulpecula999 1 year ago
i know what the answers not... lol
880330145789 1 year ago
It's 12,625,245. Am I right?
mikeusat 1 year ago
What I don't understand is why you say there are so many variations. I mean: you say "assuming best play," that does not leave many variation from the solution you already gave. I can't see any variation before black move 21. What am I missing?
TyYann 1 year ago
@TyYann Black can decided what order to move the pawns on the side in (not necessarily one against the other) and what order to sac the knights in, as well as white have the pawn option for one brief turn which the author didn't mention. The bishop and pawn add multiple angles of checkmate which makes the number of combinations of moves and permutations ridiculous.
HiImBobBum 1 year ago
144 variations?
nicocola1 1 year ago
@philnoll @TheOnlyAlibaba ok, you both are right. i`m taking back my words. i`ve overlooked that pawn.
shuldiner2007 1 year ago
black can win the game. when black has all of it's pawns at h2, h3, h4, h5, the white bishop is at h1 and it's blacks turn to move. black can put his bishop infront of white's bishop blocking it off (on the g2 square), either forcing white to take it or letting white take his bishop. either way, the black pawns will reach the end and create 4 queens (at most). so white loses
jpkmiec 1 year ago
@jpkmiec Too slow. White mates using the B pawn and dark square bishop before black can stop it.
Th3NinjaSnowman 1 year ago
well, at 4:23 black should play bishop to g2 and win. do you agree ChessNetwork?
shuldiner2007 1 year ago
@shuldiner2007 Well Bxg2 followed by Bb4 and b3+ is mating.
philnoll 1 year ago
@shuldiner2007 bisshop from e1 would move to b4
then pawn to b3 and it would be over
TheOnlyAlibaba 1 year ago
Comment removed
shuldiner2007 1 year ago
Maybe their is a exponent trick to figure it out.
How many variations in a Mate in 1? Once thats figured out, How many variations in a mate in 2? and so forth.
darthvaderyoda 1 year ago
wow what an interesting, and fascinating puzzle this is
xuhughli 1 year ago
so many variables
DJtheband 1 year ago
Lol, anyone found the solution yet? I can only get as far as multiplying the number of possible combinations of the first 18 moves with the last 6, since it's impossible to move a black piece before all the pawns, except one are gone.
Both parts of the problem are very difficult. There could be millions of possible variations.
noxure 1 year ago
@brandy1music the discovered check would no longer be a threat, The bishop blocking the pawn is free to move, and once it does its checkmate in 1.
RsJingles 1 year ago
Why can't the black bishop on f1 not move to g2 once the pawn is on h3?
JuicersSuck 1 year ago
@JuicersSuck I wondered that too.
jwelihinda 1 year ago
@jwelihinda because then you wouldn't have the discovered attack from the bishop when queening. meaning you can move the bishop to b4, then pawn b3 mate.
Anichels 1 year ago
So chess is purely math and logic?Yet with style?
RealEros1 1 year ago
B-H1 waiting
bugandflea 1 year ago
This has been flagged as spam show
GERALD ANTHONY BAILLEAU
redchopin 1 year ago
THis is a phenomenal example of Zugzwang...... I'm going to set my computer overnight to see if it can figure out the answer....
misteratoz 1 year ago
If it has to start with the best move, there is only one best move and that best move has to end it in 24 moves, therefore there is only one solution. -Luis Figueroa, P.R.
0147luis 1 year ago
@0147luis No for black any move which prolongs the game to 24 moves is equally 'the best'. All those moves fall under the category of 'best play'.
jamiedastylishman 1 year ago
Its easy not even 24 moves just in 2 moves
first bishop e1-b4, then only thing black can do is d8-c6 which can be taken by bishop a8. Second, pawn b2-b3 then it is check mate. You can check it.
mashka888 1 year ago
@mashka888 WRONG!!!!!! After bishop to b4 black pushes pawn to e1 causing discovered check. Whites only move is then king to c5. Black then plays queen to b4 taking the bishop and causing checkmate.
Th3NinjaSnowman 1 year ago
@mashka888 white would lose if he made that move
gtq838 1 year ago
@mashka888 This is entirely wrong, black advances the pawn and promotes with discovered check from the bishop on f1. He even says as much in the video
greenchevalier99 1 year ago
sssssssssssssssss
shrivibhu 1 year ago
checkmate in 24 moves ? LOL now thats looking ahead .
hey jerry whats up with more of your chess matches. theres not many you made and i really enjoy watching them. can you upload some more ?
mobbinthrudabay 1 year ago
at 4:24 why doesnt black just move his bishop to g2 trapping the white bishop? White would then have to take blacks bishop and then black would just recapture with his pawn from h3
wouldnt that be a good move?
tatomuck18 1 year ago
@tatomuck18 4:24 instead of moving Black's pawn to h5, Black moves Bg2, then White moves Bb4 and it's an inevitable checkmate, no matter what.
benacostian 1 year ago
@tatomuck18 No because now the darksquarebishop can move because queening the pawn wont be giving discovered check. So Bb4 with mate to follow...
Robocop131313 1 year ago
@tatomuck18 Was the exact same thing I saw. Answer to his last question, since you have to assume best moves is zero, white never wins this game unless black is an idiot.
geheirnwaeshen 1 year ago
Where do you think those variations start? From move 18 or later?
TyYann 1 year ago 3
@TyYann The initial position. 6:49
ChessNetwork 1 year ago
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HeavyweightThinker 1 year ago
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AnotherProblemist 1 year ago
I have a solution to your "unsolved' problem. The key words in the question are "assuming best play" which you did NOT demonstrate in your given solution to the first problem. Assuming best play Black will always win! Afterblack has a pawn on h3 and the white bishop is on h1 black need only play bishop to g2, traping the white bishop. Play continues h1xg2 , h3xg2 and and black will promote to a queen next move. Should white not take the black bishop then g2xh1 and black gets a queen in 2 moves
craigberry007 1 year ago
@craigberry007 But that would be too late. If the f bishop moves, then Be1-c3 and next move b2-b3 checkmate. Watch from 3:22
TyYann 1 year ago
@craigberry007 two moves is too late. After the exchange of bishops black no longer has the threat of discovered check with the bishop and white plays Bb4. Black Queens but white then delivers checkmate with b3. I saw the same thing, but as you can see white has a reply.
Quinston82 1 year ago
@craigberry007 promoting a queen does not equal a win. i have gone over this position on my comp several times. if the if Bb2 white will still win by force
reedschel 1 year ago
im not great at chess.. but @5:10 why cant f1-g2? its protected by the pawn on h3 and it forces white bishop to take it but then pawn can keep moving.. can anyone explain why this is bad for black?
ddominatedd 1 year ago
This has been flagged as spam show
@ddominatedd Same as with tatomuck18:
No because now the darksquarebishop can move because queening the pawn wont be giving discovered check. So Bb4 with mate to follow...
Robocop131313 1 year ago
I know the solution, enter in marinachessland.webs.com. "That's not completed, I'm finishing to study the solution".
83thrillermj 1 year ago
could it have been a real match??? I mean because of the blacks pawns in the edge.
ducksaj 1 year ago
Rybka 4 could not see the win , only fritz 12 can do it......lol
ducksaj 1 year ago
I know!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Based on the Everett Theorem me and me colegues using the prolonging technique of pawns discovered gravity in 24 moves so we concluded that the solution is definetly a number! How cool is that! :p
dominicanoaki 1 year ago
jerry, "The Problemist is a mag, a source, not a "creator"
zalkorcwb 1 year ago
If you set up that position in the Chess Master 11th it will have white checkmated....:S
ducksaj 1 year ago
Nice video - Who the author of the problem?! (sorry if i'm failing to visualize, but a published Chess Problem should be accompanied by:) (a) Author (s) (b) Place and Date of first publication (c) The Prize or other nomination awarded (eventually) Thanks for the attention
zalkorcwb 1 year ago
Nobody is Perfect....I'm nobody!
manotory 1 year ago
Hmmmm I'm saying 1 only best play can result in one variation in which it takes 24 moves to mate.
TheHaylingTerrier 1 year ago
I might be the worst chess player on youtube, but I am in 8th grade math in 6th grade. so my vow is before i i will finish this problem.
AwesomeSeanable 1 year ago
37?
bierbuik 1 year ago
Thus, so far: 2^10 x 3^2 h pawn combinations. Now the final BLACK's 18-23 Moves: 18..Nb7, 19..=Last 'h'pawn promotion, 20..Bg2, 21..Nf3, 23..'e' pawn promotion ALL forceful. Move (22...Nf3 or Ne4) = 2 choices
So, Final Solution: 2^ 10 x 3^2 (h pawn combinations) x 512 promotion permutations x 2 = 2^20 x 3 ^2 = 1048576 x 9 = #9437184 different mates in 24. Hope I've helped!!
Neueregel 1 year ago
@Neueregel That seemed to helped, but what are the 5 forced moves, cause i couldn't follow? Has that to be when the bishop occupies h1 and therefor makes h1/QRBN impossible?
Is a bit hard write all number of moves sequences out i guess :(. Wonder if there are more studies like this with that much combinations that leeds to the fasted checkmate. Nice problem.
serrie85 1 year ago
@serrie85 Hey there. No, by 'forceful' moves I meant only forceful 'pawn' moves. Not knight. That means, one choice of 1 pawn moving forward each time. When these first 17-18 black's 'h' pawn moves finish (i don't remember the number exactly) , ONLY THEN the knight start to move. Remember : The goal is to prolong the Checkmate as soon as possible. Cheers.
Neueregel 1 year ago
Analytically:
1-17 Moves: All are 'h' pawn moves, since anything else leads to a quicker mate. Now move 1 is a forceful move 1..h3 . Also there are 4 other forceful h moves, when we have to avoid a row of congested pawns at g2,g3,g4 etc. So 5 forceful moves. The remaining 12 moves are always choices of 2 different pawn moves (10 times), except the cases of triplette formations of h7-h5-h3 and h6-h4-h2 where we have 3 movement choices(2 times).
Neueregel 1 year ago
BLACK's MOVES Pawn promotion permutations= 1024 (we have 5 different pawns with exponent to 4 different pieces promotions for each pawn}) So 4^5=1024. However, last 'h' pawn, on move 19 cannot be Rook or knight because it cannot control the diagonal. So 4^4x2=2^9=512 different permutations.
Neueregel 1 year ago
WHITE's MOVES: 19 forced oscillations between a8-h1(with capturing or not) PLUS the 5 forced moves 19. Bxb7, 21.Bxg2, 22.Bb4 .(23 Bxf3 or Bxe4), and 24. b3## White's Move 23 forcefully depend on black's 22nd move respectively. So White has no options, is just reacting and the problem is reduced to just the combinations of BLACK's 23 moves
Neueregel 1 year ago
Is this even possible =o getting 4 pawns on the last rank in a row! im more interested to even get to this position.
McSick1990 1 year ago
@McSick1990
it is indeed possible, tho only in a theoretical level. all the captured white pieces would have to be captured at the apropriate squares by the corresponding black pawns - except for one. the black pawns have committed 9 captures to get to this position and theres 10 white pieces missing.
TheAlnoth 1 year ago
that's easy, the black can win easly too
wasfe1 1 year ago
i have two answers for that issue...
wasfe1 1 year ago
does the total number of combinations also include black intentionally letting white promote a pawn to queen then he dinks around for like 15 moves to mate? cause if so that would be unimaginable number
godlfire 1 year ago
as the moves a pretty much set on what black and white must do the main factor that increases the variations is the location the peices moved to get captured ex... knight to e4 and knight to f3 so if you find all possible moves for each peice then multiply them together you get your answer?
godlfire 1 year ago
@Cartmansonic515 How?
darthvaderyoda 1 year ago
Ah hah! Found it. Not the answer, your video, lol. Simple enough title, I was afraid it was going to be a realization during one of your blitz games "Oh, and this current setup has the most possible outcomes," thankfully, wasn't the case. I wonder if the problem has a name?
DarkKar 1 year ago
will the black should not move his pawn from H3 to H4 he should move the other pawn from H5 to H4 and here is the possibelties after the H5 to H4:
1- E1 to H4 so the black king will pass to A5
or
2- A8 to H1 so the black will move F1 to G2, then the white E1 to B4, so the black G2 to D5 by that black will force the white king to move for C3 after that the black king will pass to B5
wasfe1 1 year ago
as a minimum the black pawns (alone!) will capture 1 Queen, 2 Rooks, 2 Knights, 4 Pawns from the white!!!
because of that the white pawns must capture 4 pieces from the black as follow: (1 Queen, 1 Bishop, 2 Rooks)!!!
wasfe1 1 year ago
well... if you have 4 pawns in a row do you know what is that mean?! it means that you have to capture 6 peices "as minimum" from your opponent,
also you have two pawns at E6 and E2 so in order to have this arrangment you have to capture another three pieces...
so as minimum you have to capture 9 peices from your opponent with using your pawns...
if we calculat the captured pieces from the white side it will be 10 as follow: 1 queen ; 2 rooks ; 2 knight and 5 pawns
wasfe1 1 year ago
awesome video
classicmusic05 1 year ago
Man, that's really cool.
hundredandfour 2 years ago
Yea, like in a real game i'll have 4 Pawns in a raw xD
That can be cool ^_^
almoghh 2 years ago
Sent you a possible algorithm to obtain a solution.
j7caiman 2 years ago
Nice prolongment. If white were running out of time, that would be great. :D
Benson and Tonic
myspace/bensonandtonicproductions
nblfyb 2 years ago
Thanks
ChessNetwork 2 years ago
sent you solution through pm
NockLaumOK 2 years ago
WTF black can use the light squared bishop to challenge the diagonal and win.
SKYNET369 2 years ago
Comment removed
NockLaumOK 2 years ago
I just know that the number of solutions is a primer number :)
gustavonarez 2 years ago
Could be! :)
ChessNetwork 2 years ago
Are we also to assume that the white's "best move" is the bishop oscillating back and forth? You didn't specify white's "best move", you just gave your opinion. It's not really a fair question because "best move" is subjective.
VitalSigns1 2 years ago
I didn't give my opinion on the bishop oscillating. A solution was given to the mate in 24 which implies bests move since the goal is to mate as soon as possible.
ChessNetwork 2 years ago
6859776
NockLaumOK 2 years ago
@NockLaumOK Nice...proof?
ChessNetwork 2 years ago
i sent you a link to download it, didnt i?
NockLaumOK 2 years ago
@NockLaumOK I won't be doing any downloading to view a solution. Another way to view?
ChessNetwork 2 years ago
1, because if we are assuming best play, only one should be the answer as the rest would be positionally weaker. But since I know you didn't really mean "best play" literally... i will come back with another answer..
JustAnotherPers0n 2 years ago
@JustAnotherPers0n oh and this isnt a very complicated problem, just a little annoying to solve.. it simply involves a few combinations and permutations, have to account for the number of types of in between moves.. for example the knight moves in between and the pawn moves in between, so on.. basically something like X*Y*Z*T each letter representing the number of inbtwn moves for each type the only problem is.. the inbtwn moves can be interlaced with different types, just an annoying problem :)
JustAnotherPers0n 2 years ago
@JustAnotherPers0n sorry after taking a look at it again the different types of X number of moves cant be interlaced, it is pretty constricted so, but the different way to lose knights can be interlaced.. so yes disregard the last sentence.. soo X numbers of pawn*Y number of valid "best play" knight 1*2 *Z prolonging moves(bishop & others i havent taken much time to read into this position)
JustAnotherPers0n 2 years ago
I don't understand the problem. People are throwing out big numbers in the comments. What the? :(
I'm not stupid, i'm just new to chess and don't really understand what's going on...
SilentSlayers 2 years ago