Mate in exactly n moves

David113
Posers and Puzzles 24 Apr '08 19:52
1. 24 Apr '08 19:52

White to play and mate in exactly n moves. How many ways (as a function of n)?
2. 24 Apr '08 22:081 edit
The term "Fibonacci" comes to mind...

F(n) = {1, n = 1,2; F(n-1) + F(n-2), n > 2}
3. 24 Apr '08 23:21
Originally posted by Jirakon
The term "Fibonacci" comes to mind...

F(n) = {1, n = 1,2; F(n-1) + F(n-2), n > 2}
That's trueđź™‚
4. 25 Apr '08 02:08
True until threefold repetition kicks in and the game is declared a draw.
5. 25 Apr '08 10:36
Originally posted by geepamoogle
True until threefold repetition kicks in and the game is declared a draw.
According to the chess problemists' codex, in chess problems the threefold repetition law is used only in retros.
6. SwissGambit
Caninus Interruptus
25 Apr '08 16:49
Originally posted by David113
According to the chess problemists' codex, in chess problems the threefold repetition law is used only in retros.
No, that's false. You are confusing the 3-fold repetition rule with the 50-move rule.
Article 17 - 50 Moves-Rule

Unless expressly stipulated, the 50 moves-rule does not apply to the solution of chess compositions except for retro-problems.

Article 18 - Repetition of Position

A position is considered as a draw if it can be proved that an identical position [21] has occured three times in the proof game combined with the solution.

www.saunalahti.fi/~stniekat/pccc/codex.htm
7. 30 Apr '08 14:06
Originally posted by David113
According to the chess problemists' codex, in chess problems the threefold repetition law is used only in retros.
Mate in "n" moves implies that your oponent has no outs.
after at most 7 moves your oppnent has two legal moves: shuffle the bishop, declare a draw.
as the "self mate" stipulation was not indicated the game ends on move 7 where white must mate in order to avoid a draw.

Solutions to mate in 1-7 follow fibonacci