and Mate in 131 Moves
...and six other interesting problems
Edward D. Collins
(I did not compose any of these problems but the text below is all me.)
|Originally I was going to
devote this page to problems that most chess engines have
difficulty with. With many of these problems that may
still be true but I've decided to simply devote it to
"interesting" positions and problems instead.
All solutions are included and can be found to the right of each diagram. The 131 move monster I saved for last. That problem has got to be one of my all-time favorites, hence the name of this page.
Eventually I'll probably have many more positions than this... but hey, I've got to start somewhere! For now the few that I have can be found below, all on this same page. I hope you enjoy them.
Note: The Forsythe notation for each position is included underneath each diagram to facilitate setting these positions up. (Many chess programs have the ability to load FEN directly or cut an paste FEN notation into a blank board.)
White to play and win
|If it were Black's move, and did
not have the pawn on c7, then White's win is rather
straightforward. Black would have nothing better than to
check the White King on e8, which would give White an
opportunity to get his king off from his first rank.
(i.e. 1...Re8+ 2.Kf2 Rg8 3.Kf3.)
The win thus
requires a neat little triangulation maneuver:
4.Kh3 looks inviting but turns out to be a draw. (Feel free to work it out if you don't wish to take my word for it.)
White returns to the center but via a different
Ta da! We've now arrived at the diagrammed position only now it is Black to move. After 7...c6 the cycle will repeat, and then again so after 14...c5.
After 21...Re8+ 22.Kf2 Rg8 Kf3 note that your chess engine will give White a huge edge.
White to play and draw
|How can White stop the e-pawn from
The interesting solution to this problem begins with 1.Bg4! If Black takes the Bishop than after 2.f3+ either 2...Kf4 or 2...Kh4 White is able to pick up the e-pawn and the game is then an easy draw.
But what happens if Black simply ignores the Bishop and Queens the e-pawn immediately?
The Black King is now imprisoned in a nice little tomb and there is nothing that he can do about it. Black's Queen by herself will be able to make no headway at all against White's King.
With care, White can simply shuffle his King back and forth on e1, e2, e3, and f3. If the White King could ever be stalemated in the corner, then White would be forced to move the Bishop and subsequently the Black King could escape. Black is unable to force this however, and so the result is a draw.
White to play and win
|Here it is White's Bishop which
demonstrates its versatility.
If it were Black to move instead of White, and if the a7 pawn was fixed at a4 (or did not exist at all) then 1...c4, which would be forced, would create a game winning passer for White, i.e. 1...c4 2.dxc d3 3.c5 d2 4.Bxh5 Kg8 5.c6 Be5 6.Kd7 Kg7 7.c7 Bxc7 8.Kxc7 Kf6 and it's curtains for Black.
So the idea is the same as in position #1... how to lose a tempo and give Black the move?
1. Bd5! Kg6 2.Be4+ Kg7 3.Bf5 Kg8 4.Be6+ Kg7 5.Bf7.
This first cycle is now complete. After 5...a6 history will again repeat itself, and then again after ...a5 and again after ...a4. Eventually, Black will be forced to play 20...c4. After that it's all but over. After these forced sequences, the winning line is probably 21.dxc4 d3 22.c5 d2 23.Bxh5 Kg8 24.c6 Be5 25.Kd7 Kg7 26.c7 Bxc7 27.Kxc7 Kf6 28.Kd6 Kf5 29.Kd5 Kf4 30.Bd1 Kg3 31.h5 or something similar.
White to play and win
|The first move is rather obvious...
1.Nh1 is almost forced. However, after 1...f6,
if one were to examine the position very closely, we see
that if it were Black's move, then the Black
King would be forced to retreat to f7 and White could
invade the enemy camp via h5. But once again, how to lose
2.Kh3 Kf7 3.Kg2 Kg6 4.Kf1 Kf7 5.Ke1 Kg6 6.Kd1 Kf7 7.Kc2 Kg6.
Tempting is 8.Kb3 but after 8...Kg5 9.Kc4 Kh4 and either 10.Kd5 or Bxf6 it's Black who eventually wins!
8.Kc1 Kf7 9.Kd1 Kg6 10.Ke1 Kf7 11.Kf1 Kg6 12.Kg2 Kf7 13.Kh3 Kg6 14.Kh4.
The theme here is similar to positions #1 and #3. The tables have been reversed and now it is Black to move. After 14...h6 the cycle repeats:
15.Kh3 Kf7 16.Kg2 Kg6 17.Kf1 Kf7 18.Ke1 Kg6 19.Kd1 Kf7 20.Kc2 Kg6 21.Kc1 Kf7 22.Kd1 Kg6 23.Ke1 Kf7 24.Kf1 Kg6 25.Kg2 Kf7 26.Kh3 Kg6 27.Kh4
|Note that either time Black could
have kept the White King from returning to g2 by
advancing the h-pawn to h3. However, if he did so, then
Black would then also have made it impossible for himself
to advance via the Kingside and White would be able to
work his way around on the Queenside without worry.
Eventually Black's King is forced back to f7 on move 40 and it's a "matter of technique" from there.
White to play and win
|Despite the simplicity of this
problem, I'm willing to bet that many of you who read
this would NOT find the solution over the board.
White must Queen immediately.1.h8=Q and Black has no choice. 1...a1=Q. Okay, so far so good. Now, White has 17 Queen moves at his disposal, 16 of which either lose or draw!
The answer is the one and only 2.Qg8! (Not Qxa1 and the game ends in stalemate.) This is the only move that wins! White is threatening either Kd7 or Ke7 mate. Black has just one valid reply. 2...Qa2. Again, this is Black's only defense. 3.Qe8! Qa4! (Again!) 4.Qe5+! Ka8 5.Qh8!! The Queen returns to her place of birth! But now Black's Queen does not have that luxury! If 5...Qa1 then White wins with Qxa1+!
Note that 2.Qe8 would not do immediately as 2...Qg7 would then draw! Also note that 2.Qf8 doesn't work since that is refuted by 2...Qa3. 3.Qe8? Qd6+!
If this problem doesn't put a smile on your face, nothing will.
White to play and win
|Is a Bishop ever stronger
than a Queen?
Despite White's material superiority, Black is both threatening to Queen on e1 and mate on g2 with fxg2!
1.Bh2+ Kh4 (If 1...Kf2 then 2.gxf3 and Black can't Queen since the e-pawn is pinned. 3.Rb1 Kf2 4.Bg1+ Kf3 5.Re1 and White wins easily.) 2.Rxe2! fxe2 3.Bc7 e1=Q+ 4.Kh2 Qf2 5.Bd6! Zugzwang! Black is compelled to move. If 5...g4 then it's mate in two beginning with 6.Be7+. If the Queen moves anywhere along White's second rank then 6.Bg3 is mate. If 5...Qe1, then 6.g3+ leads to mate.
(Other lines beginning with 2.Bd7 instead of the immediate Rook sac lose in similar fashions.)
Update! This problem has been cooked. See my note after the problem!
White to play and mate in 131
|No, that's not a typo. It really is
White to play and mate in 131 moves.
I discovered this problem on the web quite some time ago. That site, however, did not have the actual solution available as the author (of the site) was himself unsure of it. He did give a general description of how he felt that the forced sequence should go. He was close but he didn't quite have it. However, after playing with it for longer than I care to admit, I think I've figured it out.
Black is threatening to extricate his Queen from the corner and if he does, he wins. White can therefore never allow this.
The solution begins 1.Qc5+ Kb8 2.Qe5+ Kc8 3.Qd5! Kc7 4.Qd7+ Kb8 5.Qd8+ Ka7 6.Qb6+ Kb8
At this point White can now catch his breath and take time out to play 7.Kc1 with the intent to pick up the two advanced isolated b pawns.
|Black can't play 7...Qh7 which
would allow a mate-in-one on d8. And note that at any
time, Black advancing the h5 pawn only makes things
easier for White. So Black is forced to play
7...Kc8 and now the above six move cycle repeats
8.Qc5+ Kb8 9.Qe5+ Kc8 10.Qd5 Kc7
It is important to see that each time, after Qc5+, Black only makes the cycle one move shorter with Kd8 instead of Kb8. To wit: 8...Kd8 9.Qd4+ Kc8 10.Qd7+ Kb8 11.Qd8+ Ka7 12.Qb6+ Kb8. (Likewise with Kb8 instead of Kc7. The site that I found this problem at thought the solution revolved around this shorter five move cycle instead of the correct six move cycle.)
White now has another moment to do something "constructive" and advances his King closer to the b3 pawn with 14.Kb2. The cycle then repeats and White picks up the b4 pawn this way as well:
15.Qc5+ Kb8 16.Qe5+ Kc8 17.Qd5 Kc7 18.Qd7+ Kb8 19.Qd8+
Now White plans to use his King and Queen in the same manner to pick up the jewels on c5 and h5 too. But he must be careful! A direct approach via Kc4 won't work since Black would have the opportunity to play ...b4+ after White's Queen goes to d5 in our cycle! So White must be sure to avoid that square. Note that White must also avoid d4, e3, and f2 since Black could avert the always threatened mate-in-one with ...Qa7+. So a slightly more roundabout route is called for:
Kc8 36.Qc5+ Kb8 37.Qe5+ Kc8 38.Qd5 Kc7 39.Qd7+ Kb8
Black only makes the mate shorter for White if he ever moves the h-pawn. (For a short while I thought that he could actually prolong the mate by a move by moving to h4 at the proper moment but I don't think that's the case.) It appears that he prolongs the mate as much as possible by forcing White to make as many of the six-move sequences as he can.
After picking up the pawn on h5, White picks up the pawn of f5 as well:
78.Qc5+ Kb8 79.Qe5+ Kc8 80.Qd5 Kc7 81.Qd7+ Kb8
Now White's plan is to advance both the h-pawn and the f-pawn to the fifth rank Here the order that he does so is unimportant:
92.Qc5+ Kb8 93.Qe5+ Kc8 94.Qd5 Kc7 95.Qd7+ Kb8
(Again, note that White's King can not retreat
to e4!) Kc8 106.Qc5+ Kb8
White now has a forced mate in 6, as most of today's chess engines will confirm.
126.h6 gxh6 127.f6 exf6 128.g7 Bxg7 129.e7 f5+ 130.Kxf5 Kc8 131.e8Q#
If Black did not wish to take the pawn on h6 on move 126 then White would have mated one move earlier, i.e. 126...Kc8 127.h7 Qb8 128.h8Q Qf4+ 129.Kxf4 Kb8 130.Qxf8# (Here too, the site that I found this problem at had this line reversed and thought that not taking on h6 prolonged the mate. I don't think that's correct.)
Just for fun, here is the breakdown for White:
maneuvers x 6 moves per maneuver = 108 moves with the
White to play and a forced mate in 131! Zowie!
the entire sequence in a PGN format.
If anyone can find a flaw in my analysis, please let me know. It took me quite awhile before I found the six move forcing sequence. (I didn't see the subtle non-checking Qd5 and neither did any of my chess programs.) I couldn't figure out how White proceeded if Black played his King to directly to b8 as in the main line rather than to e8 which makes things easier. (If he played it to e8 then the five forced checks were easy to find!)
Added note: I just finished playing over a dozen or so lines with a strong guest who was logged into FICS. We set this position up with the servers examine mode and he took the White pieces with the attempt to force a win even earlier. We discovered that if White attempts to go about the win via other ways, he not only is unable to, but he loses every variation.
UPDATE as of 1-6-2007 !
It appears this problem has been "cooked."
As noted in the problem, White can't move onto the a7-g1 diagonal
but it appears as if he can't move onto the a8-h1 diagonal either!
After White plays 58.Qe5 it appears Black can play 58... Kb8 instead.
White has nothing better than 59.Qd4, which is met simply with 59... b6+
(59. Kg3 doesn't work)
Thanks to Ogul Koseoglu for finding this.
Back to my Chess page