Alexlaw1964 wrote: ↑Fri Feb 28, 2025 5:39 pm
Your white king is out of place. The king can't walk!
We misunderstood each other. You wrote, 'In other positions, the white king and the free black king cannot be checked,' which I interpreted as: only with the king on c6 is checkmate possible. Evidently, you meant something else. What did you mean?
Alexlaw1964 wrote: ↑Fri Feb 28, 2025 5:39 pm
Your white king is out of place. The king can't walk!
We misunderstood each other. You wrote, 'In other positions, the white king and the free black king cannot be checked,' which I interpreted as: only with the king on c6 is checkmate possible. Evidently, you meant something else. What did you mean?
Alex
White has a king on c6 and a queen, black has a king.
We need to checkmate the black king.
Only the queen and the black king can walk.
I fear I am also missing something. In a KQk or Kkq endgame with the strong side's king unmovable, I think that the queen can force the opponent's king to {a,h} files or {1,8} ranks via knight jump method —as shown by Protej modified engine— in order to deliver the checkmate there, always if the strong side's king is on {c,f} files or {3,6} ranks, is not it? These are 28 possibilities out of 64, unless proven wrong. Other thing is that the longest checkmates are in 23 moves if the stronger side starts and these 23-move checkmates only are with the stronger side's king on {c3,c6,f3,f6} squares.
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@Kirill: I am sorry for Kirill because I feel we are somewhat hijacking his thread.
Alexlaw1964 wrote: ↑Fri Feb 28, 2025 8:26 pm
White has a king on c6 and a queen, black has a king.
We need to checkmate the black king.
Only the queen and the black king can walk.
Yes, it has been solved by my engine, see this post. Ignore the next one.
Here is the next puzzle. In 4x4 chess, the kkqqrrp ESM (endgame + side to move, meaning the bare king is to move first) has 3,534,960 unique legal positions. Among these positions, 163,610 are draws and 3,371,350 are losses. Also, according to my data, this ESM has 163,609 stalemates. This means that there is exactly one non-stalemate draw, the rarest per-ESM draw among positions that have moves (1 / 885,513), in the 2-to-10 piece subset of 4x4 chess. I've no idea what this position looks like and if it's easy or hard to find, but I am curious to see it.
Kirill Kryukov wrote: ↑Mon Mar 03, 2025 7:20 am
Here is the next puzzle. In 4x4 chess, the kkqqrrp ESM (endgame + side to move, meaning the bare king is to move first) has 3,534,960 unique legal positions. Among these positions, 163,610 are draws and 3,371,350 are losses. Also, according to my data, this ESM has 163,609 stalemates. This means that there is exactly one non-stalemate draw, the rarest per-ESM draw among positions that have moves (1 / 885,513), in the 2-to-10 piece subset of 4x4 chess. I've no idea what this position looks like and if it's easy or hard to find, but I am curious to see it.
Kirill Kryukov wrote: ↑Mon Mar 03, 2025 7:20 am
Here is the next puzzle. In 4x4 chess, the kkqqrrp ESM (endgame + side to move, meaning the bare king is to move first) has 3,534,960 unique legal positions. Among these positions, 163,610 are draws and 3,371,350 are losses. Also, according to my data, this ESM has 163,609 stalemates. This means that there is exactly one non-stalemate draw, the rarest per-ESM draw among positions that have moves (1 / 885,513), in the 2-to-10 piece subset of 4x4 chess. I've no idea what this position looks like and if it's easy or hard to find, but I am curious to see it.
