Colossus of a mate in 7

[Ajedrecista]

Hello Uri:

Yes...after 4.Qg2 there are some lines which not end in the Qa8,Qg8# maneuver...ty for clarification.

The mainline of Bogoljubow's solution was: 1.d3 cd 2.Rf4 gf 3.Ra4 Bxa4 4.Qg2 a1Q 5.Ng6 fg 6.Qa8 and 7.Qg8#

From my human point of view this line is the most obvious (even so for strelka it seems )

The first two times this problem was published ( "Deutsche Schachzeitung"and then "The Problemist") it were not solved by anyone.
Only the third time there were two correct solutions.

For a human (well the humans i know) the 1.d3 move seems nearly unfindable...and even the engines have their problems to find it quickly (instead of matesolving software).

Btw....does anyone know a problem with mate in 7 moves without zugzwang-elements for which an engine (lets say houdini, critter, stockfish, rybka) takes longer than this one ?
...a hard task i think.

Regards from germany

I remember that leonid posted hard mates for chess engines.
Here is an example

This does not seem to be good enough but maybe another position if leonid is good enough(stockfish2.2.2 4 cpu could find the mate in 31 seconds) but maybe a different position of leonid is good enough.

http://www.stmintz.com/ccc/index.php?id=154354

[d]rQ1Q1rnk/q4qbp/3nQqbB/q1Q1NnNn/5QQ1/b2Q4/1QB3Q1/1K1R3R w - -

1.Ngxf7+ Nxf7 2.Nxg6+ hxg6 3.Bxg7+ Nfxg7 4.Qgxh5+ Nxh5 5.Qfxf6+ Ngxf6 6.Qdxf8+ Kh7 7.Qgxg6#

Ugly position for my eyes! I must admit that I do not like these kind of positions... but challenge was accepted. Spark solved it!

Analysis by Spark 1.0 w32 (using two cores) in an Intel Pentium D930 (3GHz), with 128 MB of hash, running under Arena 2.0.1 GUI:

FEN: rQ1Q1rnk/q4qbp/3nQqbB/q1Q1NnNn/5QQ1/b2Q4/1QB3Q1/1K1R3R w - - 0 1

Spark-1.0-win32-mp:
1 00:00 49.423 210.310 -2,50 Ne5f3
1 00:00 75.286 209.127 -2,45 Ne5c4
1 00:00 80.022 204.659 -2,44 Ne5c6
1 00:01 219.235 200.397 -0,64 Ne5xg6+ Qf7xg6 Bh6xg7+ Qa7xg7 Qd8xf6
1 00:03 678.820 215.020 +3,23 Ne5xf7+ Qa7xf7 Ng5xf7+ Qf6xf7 Bh6xg7+ Nf5xg7 Qe6xf7
2/2 00:03 683.166 215.373 +3,23 Ne5xf7+ Qa7xf7 Ng5xf7+ Qf6xf7 Bh6xg7+ Nf5xg7 Qe6xf7
2/2 00:09 2.024.286 212.724 +7,51 Ng5xf7+ Qa7xf7 Bh6xg7+ Qf7xg7 Ne5xg6+ Qg7xg6 Qb2xf6+ Nh5xf6 Qg4xg6
3/4 00:09 2.025.656 212.511 +7,51 Ng5xf7+ Qa7xf7 Bh6xg7+ Qf7xg7 Ne5xg6+ Qg7xg6 Qb2xf6+ Nh5xf6 Qg4xg6
4/8+ 00:09 2.033.705 212.663 +7,76 Ng5xf7+ Qa7xf7
4/8+ 00:09 2.054.719 213.477 +8,01 Ng5xf7+ Qa7xf7
4/8+ 00:09 2.067.391 213.750 +9,01 Ng5xf7+ Qa7xf7
4/8 00:09 2.091.186 213.778 +9,42 Ng5xf7+ Qa7xf7 Bh6xg7+ Nh5xg7 Rh1xh7+ Bg6xh7 Qg4xg7+ Qf7xg7 Qg2xg7+ Qf6xg7 Qd8xa5
5/10+ 00:10 2.183.635 215.987 +9,67 Ng5xf7+ Qa7xf7
5/10+ 00:10 2.186.875 216.308 +9,92 Ng5xf7+ Qa7xf7
5/10 00:10 2.207.480 217.015 +10,77 Ng5xf7+ Qa7xf7 Bh6xg7+ Nf5xg7 Ne5xg6+ Qf6xg6 Qd3xg6 Nd6e4 Qg4xh5 Ng8f6 Qg6xf7
6/14+ 00:10 2.298.524 219.220 +11,02 Ng5xf7+ Qa7xf7
6/14+ 00:10 2.304.043 219.432 +11,27 Ng5xf7+ Qa7xf7
6/14+ 00:10 2.447.401 224.388 +17,27 Ng5xf7+ Qa7xf7
6/14+ 00:11 2.487.288 225.155 +23,27 Ng5xf7+ Nd6xf7
6/14 00:12 3.372.698 266.806 +M8 Ng5xf7+ Qa7xf7 Bh6xg7+ Nf5xg7 Qd3xg6 h7xg6 Ne5xg6+ Qf7xg6 Qe6xg8+ Kh8xg8 Qd8xf8+ Qf6xf8 Qf4xf8+ Kg8h7 Qf8h8+
7/15 00:57 24.875.788 434.982 +M7 Ng5xf7+ Qa7xf7 Bh6xg7+ Nf5xg7 Qg4xh5 Ng7xh5 Ne5xf7+ Nd6xf7 Qf4xf6+ Nh5xf6 Qe6xf6+ Ng8xf6 Qd8xf8+

The suggested line is different to yours but also valid.

Very good eval and pruning are basic here because there are tons of possible moves. Lots of engines crash or do nothing in this position... I guess that it is due to the high number of legal moves at first ply (142 here). Maybe those engines support a maximum of 127 different moves at depth 1, while 255 would fix those crashes (it is just a random guess).

Code: Select all

JetChess 1.0.0.0:

FEN: rQ1Q1rnk/q4qbp/3nQqbB/q1Q1NnNn/5QQ1/b2Q4/1QB3Q1/1K1R3R w - - 0 1

Perft(1) =             142
Perft(2) =           7,351
Perft(3) =         967,374
Perft(4) =      52,841,538
Perft(5) =   6,518,020,904
Perft(6) = 373,415,809,086

At first ply: 3 are king moves, 113 are queen moves, 12 are rook moves, 3 are bishop moves and 11 are knight moves.

Regarding the number of unique positions after each ply:

Code: Select all

JetChess 1.0.0.0:

FEN: rQ1Q1rnk/q4qbp/3nQqbB/q1Q1NnNn/5QQ1/b2Q4/1QB3Q1/1K1R3R w - - 0 1

Positions(1) =        142
Positions(2) =      7,351
Positions(3) =    546,555
Positions(4) = 16,653,458

Positions(5) will be around 780 million. In this case, mate in seven is equal to thirteen plies... for this reason I am amazed about how well some chess software work!

Regards from Spain.

Ajedrecista.

[Ajedrecista]

Hello again:

Positions(5) will be around 780 million.

I managed to calculate Positions(5) with JetChess, using 1.25 GB of hash and 32 steps:

Code: Select all

rQ1Q1rnk/q4qbp/3nQqbB/q1Q1NnNn/5QQ1/b2Q4/1QB3Q1/1K1R3R w - -

Count  0:      24378931
Count  1:      24377711
Count  2:      24378091
Count  3:      24378038
Count  4:      24381020
Count  5:      24376142
Count  6:      24383304
Count  7:      24376694
Count  8:      24375650
Count  9:      24379233
Count 10:      24376135
Count 11:      24384759
Count 12:      24379556
Count 13:      24379341
Count 14:      24376130
Count 15:      24380329
Count 16:      24382596
Count 17:      24377160
Count 18:      24384251
Count 19:      24378043
Count 20:      24387525
Count 21:      24378980
Count 22:      24379078
Count 23:      24378907
Count 24:      24381832
Count 25:      24381314
Count 26:      24379638
Count 27:      24376508
Count 28:      24377204
Count 29:      24383137
Count 30:      24377436
Count 31:      24386883

Positions:    780151556

780.151.556   (Positions after 5 half moves)

Time: 5974.671 s

I was quite correct in my prediction because I did a lineal extrapolation of some calculated data: with other number of steps and hash size, an overflow always occured before 10% of the total calculation was reached. Doing a lineal extrapolation for each run, I got 7.801e+8 < Positions(5) < 7.802e+8, which was very correct at the end. With a given number of steps:

Code: Select all

Number of steps = s (from 0 to s-1).

C_k = SUM(j=0,k;Count_j)
Prediction_k = [s/(k+1)]*C_k

Counts of JetChess are very similar between them, this is why a lineal extrapolation works fine.

Regards from Spain.

Ajedrecista.

[Cubeman]

This is the hardest mateproblem in 7 moves i have ever seen so far.
The queen maneuver from g8 over g2 to a8 and back to her initial starting square with mate is just impressive.

Efim D. Bogoljubow


[d]R5QK/3p1p2/1pbPkB2/4Ppp1/2p4N/2p5/p2P1R1n/8 w - - 0 1



Im sure your engines will find it (at least chest does it very quickly).
Spend a little time on that problem...its really awesome IMO

Test Hiarcs 13.1 on cell phone and it found the Mate #8 with Qxg5+ quite quickly at D=11, Time=47 seconds but it took quite a while to find the Mate #7 with 1.d3 (#7) Depth =17, Time= 28 min and 24 seconds. It gives a main line as 1.d3 cxd3 2.Rf4 gxf4 3.Ra4 Bxa4 4.Qg2 Bc6 5.Qxa2+ Bd5 6.Ng2