Author: Bruce Moreland
Date: 22:29:44 09/18/00
Go up one level in this thread
On September 18, 2000 at 20:43:56, James B. Shearer wrote:
>On September 18, 2000 at 17:28:56, Bruce Moreland wrote:
>
> <snip>
>
>>The above might have bugs. If not, it's the worst case with white to move, mate
>>in 47. This looks like a harder case than the standard 8 x 8 board, since black
>>can start out in a corner, constrain white for a bit, then evade to the center,
>>since, I presume, the knight is too slow to catch black. In the 8 x 8 version,
>>black starts out in the center in the worst case.
>>
>>KR vs K is a mate in 21, and KQ vs K is a mate in 12.
>>
>>I can't do a 9 x 9 board as easily as a 10 x 10 board, but I think it may be
>>possible that you could have a "wrong" bishop in KNB vs K with that sized board,
>>so it could be a draw in some cases.
>>
>>bruce
>
> This is interesting. How about Q vrs R?
> 47 moves isn't as many as I would have guessed and makes me suspect you can
>mate with B and N on any board with a corner of the right color. 12x12 would be
>the next case to try.
> James B. Shearer
[FEN "r54/55/3k51/55/55/55/55/55/55/K1Q7 w"]
{
a b c d e f g h i j
+---+---+---+---+---+---+---+---+---+---+
10| r |///| |///| |///| |///| |///|10
+---+---+---+---+---+---+---+---+---+---+
9 |///| |///| |///| |///| |///| | 9
+---+---+---+---+---+---+---+---+---+---+
8 | |///| |/k/| |///| |///| |///| 8
+---+---+---+---+---+---+---+---+---+---+
7 |///| |///| |///| |///| |///| | 7
+---+---+---+---+---+---+---+---+---+---+
6 | |///| |///| |///| |///| |///| 6
+---+---+---+---+---+---+---+---+---+---+
5 |///| |///| |///| |///| |///| | 5
+---+---+---+---+---+---+---+---+---+---+
4 | |///| |///| |///| |///| |///| 4
+---+---+---+---+---+---+---+---+---+---+
3 |///| |///| |///| |///| |///| | 3
+---+---+---+---+---+---+---+---+---+---+
2 | |///| |///| |///| |///| |///| 2
+---+---+---+---+---+---+---+---+---+---+
1 |/K/| |/Q/| |///| |///| |///| | 1
+---+---+---+---+---+---+---+---+---+---+
a b c d e f g h i j
}
1. Kb2 { Kb1 } Rb10+ 2. Ka3 { Ka2 } Ra10+ 3. Kb4 { Kb3 } Rb10+ 4. Ka5 { Ka4 }
Ra10+
5. Kb6 { Kb5 } Rb10+ 6. Ka7 { Ka6 } Ra10+ 7. Kb8 { Kb7 } Rb10+ 8. Ka8 Rb6 9.
Qd2+
{ Qe3, Qf4, Qc5 } Kc7 { Ke7 } 10. Qa5 Kc6 11. Qf5 { Qh5 } Kd6 12. Qg6+ { Qf6+ }
Kc5 13. Qg1+ Kc6 { Kb5 } 14. Qe3 Rb5 15. Qe8+ Kb6 16. Qd7 { Kb8 } Ra5+ { Rj5,
Kc5 } 17. Kb8 Rc5 { Rj5 } 18. Qe6+ { Qb7+, Qf7 } Rc6 19. Qd5 { Qe5, Qe3+ } Rc5
{ Rc3 } 20. Qe4 Rc1 { Rb5, Ka5, Ka6 } 21. Qb7+ { Qe9+ } Ka5 22. Ka7 Rc4 23.
Qb6+ Ka4 24. Ka6 Ka3 25. Qb1 { Qd6+ } Rb4 26. Qc2 { Qd3+, Qd1 } Ra4+ 27. Kb5
{ Kb6 } Rb4+ 28. Kc6 Rb3 29. Qe4 { Qc1+, Qc4, Qc5+ } Rc3+ 30. Kb5 Rb3+ 31. Kc5
Rc3+ 32. Kd4 Kb2 33. Qe5 Kb3 { Kc2 } 34. Qb5+ Kc2 35. Qa4+ Kb2 36. Qb4+ Rb3 37.
Qd2+ Kb1 38. Kc4 Rj3 39. Qf4 { Qd9, Qg2 } Ra3 40. Kb4 Ra2 41. Qe4+ Kb2 42. Qd5
Kb1 43. Kb3 Rb2+ 44. Ka3 Kc1 45. Qh1+ Kc2 46. Qg2+ Kd3 47. Kxb2 Kc4 48. Qe4+
{ Qc6+, Qj5, Qg5, Qg8+, Qd2 } Kc5 49. Qe6 Kd4 { Kb5 } 50. Kb3 { Kc2 } Kc5
{ Kd3 } 51. Qd7 { Kc3 } Kb6 52. Kc4 { Kb4 } Ka6 53. Kc5 Ka5 54. Qb5# { Qa10#,
Qa7# } 1-0
This is the only worst case.
The general case *is* won, there are very few draws. I don't think I'm going to
try 12 x 12, since it will take me a few hours to generalize my thing further.
bruce
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