# [Retros] rstan

Francois Labelle flab at wismuth.com
Fri Nov 8 13:39:59 EST 2013

On 10/02/2013 08:53 PM, Richard Stanley wrote:

> One could also look at "half proof games" with various conditions. For

> instance, does there exist such a game that ends in mate by a pawn

> promoting to a knight? The moves of the side being mated are specified.

I used a computer to enumerate all "half games" up to 4.5 moves that end
in checkmate. This allowed me to find problems that satisfy some
conditions. For each task below I minimize the length, then the number
of captures.

- mate by a queen (15 problems in 3.0 moves, 3 problems without captures
below)
1. e4 ... 2. Ke2 ... 3. e5 ...#
1. e4 ... 2. e5 ... 3. Ke2 ...#
1. f3 ... 2. Kf2 ... 3. Ke3 ...#

- mate by a bishop (3 problems in 3.5 moves)
1... f6 2... h5 3... Rxh5 4...#
1... h5 2... Rxh5 3... f6 4...#
1... h5 2... f6 3... Rxh5 4...#

- mate by a knight (2 problems in 4.0 moves)
1. b3 ... 2. Ba3 ... 3. Bxe7 ... 4. c3 ...#
1. b3 ... 2. Ba3 ... 3. Bxe7 ... 4. c4 ...#

- mate by a pawn (11 problems in 4.5 moves, 2 problems without capture
below)
1... f5 2... Kf7 3... Kf6 4... Kg5 5...#
1... f5 2... Kf7 3... Kg6 4... Kg5 5...#

- mate by a rook (211 problems in 4.5 moves, 2 problems with 2 captures
below)
1... c5 2... Qc7 3... Qh2 4... Qh1 5...#
1... c6 2... Qc7 3... Qh2 4... Qh1 5...#

- mate by promoting to a queen (103 problems in 4.5 moves, a selection
of 3 problems with 2 captures below)
1... Nc6 2... e6 3... Qf6 4... Ke7 5...#
1... d5 2... Qd6 3... Bf5 4... Bc2 5...#
1... e5 2... Qh4 3... Kd8 4... Qh2 5...#

Remains to find:
- mate by promoting to a knight (Richard's original question)
- mate by a king
- mate by castling
- mate by en passant
(some of these might be impossible).

The exhaustive search also produced some statistics. Below, for each length:
- the number of checkmate half game problems with a unique solution
- the number of checkmate proof games with a unique solution (for
comparison)

2.0: 0 0
2.5: 0 3
3.0: 15 51
3.5: 78 1106
4.0: 2742 3813
4.5: 10042 47300

I was hoping that by extrapolating I would be able to tell whether the
genre has more "composing power" than proof games, but I still don't know.

And to finish, the most cooked problem in <= 4.5 moves:
1... g5 2... c5 3... h6 4... f6 5...#

White has 87906 ways to checkmate!

François