12 ms·
A chess position to defeat computers?
- hoagiefest 10y agocould this info, once cracked, simply be fed to the machine?
- ars 10y agoObviously. The question is why can't the machine figure it out itself.
- yaakov34 10y agoThe position nearly plays itself - none of the black pieces except the bishops have any legal moves, so if white moves his king around, without capturing anything, a draw will result by the 50 move rule (the bishops can't mate the king, since they won't control any light squares). For black, the play is even more automatic, since moving the bishops back and forth on the dark squares is the only legal option. I do think that a computer will play this correctly for both black and white; for white, a capture will result in a checkmate within a few moves, which the computer will be able to see. So this may result in incorrect computer evaluation, but not in incorrect play.
- Jtsummers 10y agoThanks for pointing out that those were bishops in the diagram. I found it difficult to parse the drawing for some reason.
- dsp1234 10y agonone of the black pieces except the bishops have any legal moves, Why couldn't black move the topmost pawn forward?
- ianpurton 10y agoBlack is moving down the board.
- yaakov34 10y agoForward for black pawns is down, in a standard chess diagram; white's side of the board is at the bottom. So black pawns have no legal moves, while the white pawns could move (the topmost pawn) or capture either of the black rooks, although this would be disastrous for white, as the black pieces would then be able to leave their position and would checkmate white in a few moves.
- fosco 10y agoKing is in way, only pieces black can move are bishops. The orientation of board is white started on bottom and black on top. Quick thing to also remember is that the bottom right square should always be white.
- nthcolumn 10y agoHe cannot move his king out of its way first due to check from the white pawn if that is what you mean. The article makes it sound like a difficult problem with some super prize. I can't believe that a chess program can't figure out it doesn't have any meaningful moves left.
- jonwachob91 10y agoHow does this account for the black pawns playing in the same rank? To me it looks like a board transformation occurs, resulting in a left-to-right movement as opposed to a up-to-down movement.
- dmichulke 10y agoBlack abc pawns are in their original file. d and e pawns captured pieces to get to a and b. Two of the three remaining pawns promoted to a bishop.
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- grondilu 10y agoAgreed. An example where a human easily finds a win while a computer fails would be much more convincing of the point Penrose is trying to make. Anyway this position reminds me of the fact that if there is any kind of situation where computers struggle it's exactly these kinds : where everything is closed apart from a few pieces. IIRC that was exploited by grandmaster Hikaru Nakamura few years ago for his handicap match against chess engine Komodo.
- ouid 10y agoyes, but the question isn't if a computer will play correctly given the position, it's "will the computer force this position as white, if it's the best move?" which relies on it's evaluation of the position.
- yaakov34 10y agoIt's not really a position you can force from further away than one move, since it would require complete cooperation between the players to create such a position. But yes, given a chance to get into this position, sure it will - e.g. given https://en.lichess.org/analysis/8/p7/kpP5/qrp1b3/rpP2b2/p5b1/PP2K3/8_w_-_- https://en.lichess.org/analysis/8/p7/kpP5/qrp1b3/rpP2b2/p5b1..., it will correctly play b3 and force the original position, since everything else results in a mate that it can see. All it needs for correct play is to rank the alternatives in the right order, and mate ranks below playing on with a material disadvantage.
- ouid 10y agohttps://en.lichess.org/analysis/8/p7/kpn5/qrpPb3/rpP2b2/pP4Q1/P3K2b/8_w_-_- https://en.lichess.org/analysis/8/p7/kpn5/qrpPb3/rpP2b2/pP4Q... here's a preceding position which stockfish completely fails to play correctly.
- yaakov34 10y agoYeah, that's a great enhancement to the original - having the queen around lets the computer avoid mate for longer than its horizon, so it prefers keeping the queen. Then again, I am not sure the computer will lose in even this scenario - it has so many queen checks that my evaluation of this position after 10 minutes of playing with it is "screw it", although I feel there has to be some way of punishing it.
- ouid 10y agowell you're playing against a computer that doesn't understand the position, black should simply disentangle his pieces, he can sacrifice almost everything he has and still win in this position, even if white is allowed to keep the queen. He can sacrifice a queen and a rook to this end, easily. how I play the position as black is Ne7 followed by Bd6. if white plays Qh4, I can play nd4+ followed by nf5 and nd6, and my king is safe. and I can slowly, safely, extricate myself and win.
- deleted 10y ago[deleted]
- 33W 10y agoThere's the white win if black blunders. If white moves the forwardmost pawn ahead and black does not capture it with the bishop (the blunder), then promoting the pawn to a queen or bishop is checkmate.
- TorKlingberg 10y agoThe claim that computers cannot solve this problem is never really clarified. Which chess AI's exactly? That it involves Roger Penrose and claims about special abilities of the human brain only makes me more suspicious.
- iainmerrick 10y agoOkay, here's my answer: all of black's pieces are blocked except for the bishops. The black king can't move without being checked by a pawn. All the black bishops are on black squares (meaning two must be promoted pawns -- unlikely but possible) So the white king just needs to stay on a white square to stay safe. The so-called "aha!" moment was remembering that bishops always stay on the same color. I can't claim any great insight, it's just something I read somewhere (so it could certainly be programmed into a computer). I had to check that there was no way for the other pieces to escape. I'm not good at chess, so I just did a very quick check and then assumed it was probably fine -- given the nature of the puzzle it's unlikely there'd be a tricky edge case to cover there. The thesis seems to be that a computer could never develop and use general theorems that let you short-circuit the search process. That's probably true for chess engines (and also mostly irrelevant to real chess matches, rather than puzzles). Definitely an interesting question to explore. My guess would be that real computer creativity is possible, but may require some new techniques.
- ars 10y agoKeep in mind, they are not looking for the answer to the chess question. They are trying to understand what it is about humans that makes them instantly able to figure out how to figure out the answer. Humans can learn, computer can't. They can train on data, but so far none can teach themself how to train.
- thaumasiotes 10y ago> All the black bishops are on black squares (meaning two must be promoted pawns -- unlikely but possible) Is this possible outside the context of purposely making bad moves to humiliate your opponent? I thought you got to choose whatever officer you wanted, which would mean bishops are strictly dominated by queens.
- pjungwir 10y agoUnderpromotion is real thing and has its (very rare) uses. Even underpromoting to a bishop can turn a draw into a win: https://en.wikipedia.org/wiki/Promotion_(chess)#Bishop_underpromotion https://en.wikipedia.org/wiki/Promotion_(chess)#Bishop_under...
- jlebrech 10y agoso it's the halting problem? https://en.wikipedia.org/wiki/Halting_problem https://en.wikipedia.org/wiki/Halting_problem
- umanwizard 10y agoHow is this related to the halting problem? I'm not seeing it.
- jlebrech 10y agounless you catch 50 moves it's a runaway algorithm
- umanwizard 10y agoThe fact that a particular algorithm never halts is only tangentially related to the halting problem. It's even possible to write non-halting algorithms in non-Turing-complete systems for which the Halting problem doesn't hold.
- sweeneyrod 10y agono
- CJefferson 10y agoNo chess problem on a standard board can be the halting problem, because the halting problem requires an "infinite space". I could, in principle, play out all possible states you could reach from this position as a giant graph, and then look to see which path is best by brute force. There are chess-like problems which invoke the halting problem, but they involve infinite boards with infinite numbers of pieces on them.
- nippples 10y ago> The institute is also hoping to develop new technology to improve the treatment of brain disease and anesthetics, develop a new type of telescope to detect dark matter and even resolve the Schrodinger’s Cat paradox, which suggests a cat in a box could be alive and dead at the same time. This is why I dislike most science reporters.
- mrfusion 10y agoI can't tell which way the board is oriented? Where did white start?
- ianpurton 10y agoIn chess illustrations white is always at the bottom.
- umanwizard 10y agoBy convention, chess diagrams are presented with White's home rank on the bottom and Black's on the top.
- anonymousiam 10y agoKing to bishop 3.
- buzzy_hacker 10y agoThe draw is fairly easy but the author mentions a win. Any ideas?
- edko 10y agoWhite cannot force a win. However, if it manages to move the king to D7, and the black bishops leave the B8-H2 diagonal (a huge blunder), then white can move its pawn to C7, and checkmate in the next move, by crowning the pawn into a queen.
- georgefrick 10y agoIt's actually a shame, they failed to remove the obvious hint for this, which is the green x drawn on the hand drawn version of the puzzle.
- ikeboy 10y agoWhy would it need to move the king? As long as the bishops move, moving the pawn and turning into queen or bishop wins.
- edko 10y agoOnce the pawn moves to C7, black's king can play to B7. If white's king were not defending, black would be able to capture the promoted pawn in the next move.
- ifdefdebug 10y agoBut while a chess engine apparently can't see the draw as long as there is a possible helpmate on the board, it can see the danger of leaving the diagonal so will never play this.
- irixusr 10y agoWhy not? Once you're on D7 the pawn can be captured or kept. If black moves to capture the pawn with a bishop, you move the king into pawn's old spot. You capture the black rook with the other pawn for the win. If there are no more bishops on the diagonal, or if they move their king to the B column, then you get a Queen and finish them off. Am I missing something (I'm a very bad player)?
- CalChris 10y agoRybka v Nakamura is this sort of anti-computer strategy where the computer clearly doesn't understand the position. 270 moves of Naka calmly moving back and forth behind a blockade, the exchange down. Rybka eventually tries to do something since it's up on material. And then it just gets slaughtered. http://www.chessgames.com/perl/chessgame?gid=1497429 http://www.chessgames.com/perl/chessgame?gid=1497429
- umanwizard 10y agoI must be missing something... isn't it impossible for black to win no matter what white does with her king (as long as she doesn't move her pawn)?
- iainmerrick 10y agoThat's the answer they're looking for. (White could still lose by making really bad moves, but so could black.)
- umanwizard 10y agoI thought it would be more complicated than that, as they really play up the "puzzle" aspect of the article (even offering a prize!)
- waisbrot 10y agoThe claim here isn't that computers couldn't solve this, just that they currently don't. In general, computers and humans play the beginning and ending of chess games with some strong heuristics -- there are too many possible moves to enumerate, but there's a very limited number of worthwhile moves to consider. In this puzzle, we have an extremely weird end-game. Humans can come up with a new heuristic on the fly, but current chess programs find all their existing heuristics fail and have to resort to brute-force search or really dumb heuristics and neither is helpful. Obviously, it would be a matter of minutes to code up a new heuristic to detect this case. The interested question is what the humans are doing that lets us solve the problem so rapidly.
- sounds 10y agoIt might be possible (I haven't checked thoroughly) to draw a parallel: "Humans can come up with a new heuristic on the fly" for this chess problem <=> "Identify the incomplete part of this system -- in the sense of Gödel's incompleteness theorem". So it might just be that humans process the game at a semantic level where we have developed the semantic tokens that can express the incompleteness, and from that produce a hypothesis, a heuristic. Computers do not, generally, apply semantic reasoning to problem solving. At least, not yet. :)
- kirse 10y agoThe interested question is what the humans are doing that lets us solve the problem so rapidly. The need for strategy is eliminated with tactically perfect play... Since computers are not yet to the point of having "solved" chess to tactical perfection, there will always be scenarios where strategy wins. IMO this is the maximum win for human-machine interaction... humans define the strategy, and computers aid in the tactical execution of that strategy. I'm not really a big believer that AI is anywhere close to beating humans at being human, especially when you step outside the bounds of a simplistic game with a narrowed rule-set. Like with cars and planes, you won't ever see an autonomous vehicle winning a World Rally Championship, and you won't ever see a computer figuring out how to make a Hudson river emergency landing. But computers can greatly assist with the braking, shifting, adjusting flaps, engine management, etc...
- dmichulke 10y agoAssuming the bishops stay on their bottom-left to top-right diagonal, you could move the king to b1 and then white b3xa4 black Qa4 (queen is forced because otherwise a4xb5 mate)
- yaakov34 10y agoThat would lose - it would not be a stalemate, no matter where the bishops are, since white has pawn moves; and starting with the next move, black would begin checking white and will quickly checkmate.
- dmichulke 10y agoYes, not sure how I could overlook that pawns, just assumed them all blocked
- selfsimilar 10y agoI don't play chess regularly but the stalemate was obvious to me immediately and the mate after about 3 minutes. Kinda clever but I'd be surprised if a chess AI couldn't see this. Penrose is notorious for thinking that consciousness depends on some spooky quantum effects that machines cannot capture (See Emperor's New Mind).
- ythn 10y agoIsn't it already a stalemate? As long as the king never leaves white squares, he will never be in danger, and thus the game will be a draw by the 50 move rule. I don't see how mate is possible. In order to mate, you need to advance the white pawn to promotion, but it's impossible to advance the white pawn without one of the 3 bishops killing it.
- nathanm412 10y agoHis rules seem to require only that the move was legally possible, not necessarily likely. Maybe after moving around the board for a while, the bishops aren't readily able to strike at the pawn.
- klodolph 10y agoTechnically, a stalemate is a draw and the 50 move rule is a different way to get a draw.
- mdpopescu 10y agoBlack can offer his bishops to the white king for free, in order to delay the draw (it's 50 moves without pawn moves and without captures [1]). However, if black offers all 3 bishops, then white could help promote the pawn. [1] https://gameknot.com/help-answer.pl?question=44 https://gameknot.com/help-answer.pl?question=44
- umanwizard 10y agoThat's not what stalemate means. Stalemate means the current player has no legal moves but isn't in checkmate. White has legal moves. It's a drawn position with good play by both sides but not a stalemate.
- erelde 10y agoI'm more interested in how the board got this way.
- vinchuco 10y agohttps://en.wikipedia.org/wiki/Retrograde_analysis https://en.wikipedia.org/wiki/Retrograde_analysis
- deleted 10y ago[deleted]
- ChuckMcM 10y agoInteresting, it took me reading the comments to realize the board orientation vs the piece movement. Like many people the fact that the black bishops are basically unable to attack anything stands out, and given the orientation that none of blacks other pieces can move. Once you see those two things, the solution does just pop out.
- UweSchmidt 10y agoCan anyone with a chess engine handy confirm the claims in the article and explain what your engine is trying to do? I wouldn't be surprised if at least some engines have some kind of conservative heuristics built in, like "If I can't find something good after x cycles, let's play something safe." and "If the opponent isn't gaining any ground after several turns of me buying time, it is likely going to be a draw even though I don't know why."
- CJefferson 10y agoIf you actually play this state in a chess engine they play it "correctly", they just can't tell what the final outcome is going to be.
- ouid 10y agohttps://en.lichess.org/analysis/8/p7/kpn5/qrpPb3/rpP2b2/pP4Q1/P3K2b/8_w_-_-#0 https://en.lichess.org/analysis/8/p7/kpn5/qrpPb3/rpP2b2/pP4Q...
- deleted 10y ago[deleted]
- overlordalex 10y agoIf anyone wants to play with this, here is the board in lichess: https://en.lichess.org/analysis/8/p7/kpP5/qrp1b3/rpP2b2/pP4b1/P3K3/8_w_-_- https://en.lichess.org/analysis/8/p7/kpP5/qrp1b3/rpP2b2/pP4b...
- ifdefdebug 10y agoConstantly valuating at about -30... Crazy enough, every chess player in the world can see immediately it's a draw from the very beginning, unless white concedes a helpmate, yet stockfish doesn't get it...
- yaakov34 10y agoTrue, but the engine does see that a pawn move by white results in checkmate in a few moves, so it would actually play this position correctly and get a draw, despite the huge negative evaluation.
- ajennings 10y agoI played it out on lichess.org. After 47 moves, Stockfish sacrifices a bishop to keep the game going. I was wondering if it would repeat that 47 moves later, but it didn't. Settled for the draw.
- mjhoy 10y agoThis reminds me somewhat of an interesting recent video from GM Simon Williams [1], analyzing a queen sac from a real game. He disagreed with the computer's favoring black, and my very uneducated guess about this is that the position is odd enough -- white is down a queen and an exchange, but all of black's pieces are tied up in defense -- that a GM can better understand the implications. [1]: https://www.youtube.com/watch?v=-YX17fljs4E https://www.youtube.com/watch?v=-YX17fljs4E
- robertlagrant 10y agoThis just seems like an odd edge case on the 50 move stalemate rule, because it's such an unusual thing to shoot for to achieve a draw that a chess program doesn't normally bother to look for it. Doesn't seem that useful a demonstration, except for people who don't know much about computers. Is this a bit like Hawking on AI?
- umanwizard 10y agoYou mean draw, not stalemate. A stalemate is one particular type of draw that has nothing to do with the 50 move rule.
- deleted 10y ago[deleted]
- c3534l 10y agoI must be pretty dumb because the solution to the problem isn't "obvious" at all, nor do I see how this proves quantum intelligence.
- JamilD 10y agoI have a hard time believing that a chess computer wouldn't draw this game… the main issue is in the centipawn evaluation function which would show black ahead. This doesn't seem like a difficult thing to correct, and it might not even be a bad idea to have an evaluation function show black ahead in that position. Practically, this isn't really an issue. In fact, running the position through the GarboChess JS engine (http://analysis.cpuchess.com http://analysis.cpuchess.com), playing as white, it just moves the king around — exactly what a human would do to draw the game.
- gweinberg 10y agoThe heuristic would probably show black as ahead, but it would also show that black can make no progress. So it's an obvious draw.
- gweinberg 10y agoI think the claim that this position would defeat a computer is nonsense. Any decent program would draw as white.
- zwischenzug 10y ago'The chess problem - originally drawn by Sir Roger - has been devised to defeat an artificially intelligent (AI) computer but be solvable for humans.' I take issue with that statement. All chess engines I'm aware of will correctly play out the draw, so it doesn't defeat them. The engines will _evaluate_ a material advantage for black. Frankly, this isn't really a surprise. Incidentally I once won money on Betfair (a P2P betting site) by evaluating a position in a Kasparov vs computer game that looked like a win to computers for the computer, but that I knew Kasparov would prevail in. My fellow gamblers were trusting the computer evaluations :)
- ouid 10y agowill a chess engine, as white, enter this position from any of the possible preceding positions?
- zwischenzug 10y agoWhy does that matter?
- ouid 10y agohttps://en.lichess.org/analysis/8/p7/kpn5/qrpPb3/rpP2b2/pP4Q1/P3K2b/8_w_-_-#0 https://en.lichess.org/analysis/8/p7/kpn5/qrpPb3/rpP2b2/pP4Q... stockfish loses here, but could easily draw.
- tunesmith 10y agoI think you just push the king around on white squares, hope all three bishops eventually blunder off the same diagonal (come on), and promote that c6 pawn to a queen. That's not a very satisfying "mate" solution but I don't see anything more clever. Reading other comments, I see you'd also need to use the white king to guard the white pawn at c7 - I missed that - but even with that, you'd still need to hope that all three black bishops would go off that diagonal. Anyway, this seemed mostly about visual pattern recognition and thinking geometrically, visualizing vectors, seeing unblocked pathways. That's not how computers do it.
- twinkletwinkle 10y agoThere's sort of a silly argument as to how you could get mate. If a computer is playing black, it reads the board as greatly to its advantage. So when it's coming up on the 50-move draw, it might offer you a bishop to take to prolong the game. It has such a material advantage, a draw "feels like" a bad outcome, so it's worth giving up some material to continue the game and go for the win. Which is a very computer way of "thinking". Once you take all 3 bishops in this manner, you promote the pawn and get checkmate.
- tyilo 10y agoOnce you take all 3 bishops it is a draw as black can't move any pieces.
- ranprieur 10y agoThis is a terrible puzzle. I'm glad I didn't rack my brain for hours looking for the "flash of insight" when all I had to do was be reminded of the 50 move rule.
- umanwizard 10y agoThe 50-move rule is a hack and the wrong way to think about it. What's really going on is "black can never force a win, therefore the position is drawn".
- toolslive 10y agoI bet machines will have a hard time with Blathy's mate in 290 too. https://www.chess.com/forum/view/more-puzzles/longest-checkmate-problem-290-move https://www.chess.com/forum/view/more-puzzles/longest-checkm...
- mark_l_watson 10y agoI remember coming home from the 1982 AAAI AI conference with my "AI, it is for real!" and thinking of how little skepticism about AI that I heard at the conference. Years later I bought Penrose's book "The Emperor's New Mind: Concerning Computers, Minds and The Laws of Physics" to 'know the enemy', but over the years I have started to agree more with Penrose's position on AI.
- vcdimension 10y agoCan white get a stalemate in 7 moves instead of 50 by just moving its king next to the black king? or is that not allowed?
- geuis 10y agoI'm just an amateur chess player. How does black have 3 bishops on the board?
- DuoSRX 10y agoBlack promoted 2 of his pawns to bishops.
- tommymachine 10y agoThis chess position doesn't defeat computers. A decent engine will draw this every time. But the disparity in the efficiency of line of reasoning (a humans' being much more efficient than a computers for this problem) illustrates the value add of a programmer to a computer, and what the job of computer programming really is. Computers basically know nothing--which is good and bad. It's good because they don't require much convincing before performing boring, repetitive tasks. They simply don't know or care that a given task is repetitive or boring, or even useful or not useful, so they will keep chugging along until they can return their output. The downside of this is that if they are to know anything at all, they must be programmed to know it. They can also learn through evolutionary iterations once programmed conceptively. One could conceive of a computer program that would spit out random logical relationships to describe a large set of data, (what humans might refer to as "life experiences") and prune the logical statements until they eventually returned accurate logic describing the data. But this would require large quantities of generations for pruning, and careful programming of heuristics for logical evaluation at inception. We can observe that our brains are born out of a system of evolution that has already undergone such processes. We have had a powerful survival heuristic on our genetic program for developing a broad set of skills, including logical reasoning, and it has been running for billions of years, pruning countless generations to give rise to our inherent level of intelligence that can discover logical shorcuts like the one in this problem. The evolutionary process also gives rise to possibly illogical but robust sets of skills, since survival and procreation are hueristically more valuable than being logically perfect in reasoning. Sure, theoretically, and given sufficient computing resources and time, a man made computer system could approximately match and even exceed the human capacity for discovering logical shortcuts. But when paired with a competent human programmer, or team of programmers, the programmers can vastly reduce the time and resources required to achieve this process of intelligent evolution, and produce intelligent programs much more quickly than a computer program left to simply evolve it's intelligence on its own. It took us humans quite a while to get here. Why would we assume that a computer could evolve faster than us, autonomously, without being programmed by us to do so? It is possible I suppose, but it's even more unlikely than the evolution of human intelligence, which sure, it happened autonomously, but over a course of billions of years.
- 10y ago
- GuB-42 10y agoAn important thing to consider is that this puzzle is designed by a human for humans. The way we solve this problem is not by thinking in term of pure chess logic. We solve it by thinking "what did the puzzle creator thought". So we recall from memory what kind of patterns are suitable for such a problem and start a tree search. It is similar the what a chess AI does but nodes are abstract patterns rather than just chess moves. This puzzle follows a mental pathway that is common for most humans. We could also design problems that can easily be solved by specific chess AIs but not by humans or other chess AIs : just make it so that the AI naturally moves in the right direction, for example by making specific heuristics always right. So while this problem is interesting for getting insight into the way humans solve puzzles, it doesn't make the human brain special.
- samiru 10y agoThis is not a "hard" problem. It is just a problem you can't solve with brute force.
- Overtonwindow 10y agoAs long as the King stays on white squares it will result in a draw in 30 moves... -shrugs- I think the computer could see this. It would revert to the rules that it knows. It would know +1, +2, +3.. and so forth moves down that it is growing closer to the draw line. It will wait for a pawn move from White. Without a pawn move... draw.
- ouid 10y agoHere's a position derived from the one shown in which stockfish plays white incorrectly. https://en.lichess.org/analysis/8/p7/kpn5/qrpPb3/rpP2b2/pP4Q1/P3K2b/8_w_-_-#0 https://en.lichess.org/analysis/8/p7/kpn5/qrpPb3/rpP2b2/pP4Q...
- TempleOS 10y agoIt's trivail for God. He went through the AI singularity a billion years ago. He solved chess. God says... versified alphabets coalesces fled arroyo's granny's Phrygia moneybag's overabundance's débutantes mow Hagiographa's plundered insurrection hardbacks socials anthropoid's bootleggers suffragan elocution's sponsorship's admonition sap's sunflower's chalet's Hayden's smirching liking's mischief's anticlockwise blithely hunted
- aaron695 10y agoAll this might prove is that humans are less intelligent. We are we wasting brain and heuristics solving problems that would never exist in real chess play? Seems like an inefficiency to me. An artifact from our lack of ability to play chess as intelligently as machines. Just like an inferior machine might be able to do something like burn outs because it doesn't have antilock braking. (I don't get cars insert real example here)
- ingmarheinrich 10y agoWhite King goes to a8, only using white squares and b8. Black has to make the mistake to leave b8 unguarded for one move. Then white pawn to c7. Black King cannot b7 because of the white King on a8. Black bishop has to take the pawn, or pawn c8Q will be mate. Black bishop on c7 however is forced stale, since the white King cannot move.