Add two black pawns to this position to form an illegal position that becomes legal on the removal of either one of them.
competition/games/chess/impossible.pawns New
New entry, edited from material collected for the archive and not yet in a released version.
Problem
Add two black pawns to this position to form an illegal position that
becomes legal on the removal of either one of them. Now do the same for
three. Now do the same for four. [ Editor: the solutions go on up
to eight pawns. ]
8 - - - - - - - -
7 - - - - - - k -
6 - - - - - - - -
5 - - - - - - - -
4 - - - - - - - -
3 - - - - - - - -
2 - K - - - - - -
1 - - - - - - - -
a b c d e f g h
This is a modification of a problem originally by T. R. Dawson, 1933.
Show solution
[ Editor: two, three and four pawns: ]
8 - - - - - - - -
7 - - - - - - k -
6 - - - - - - - -
5 - - - - - - - -
4 - - - - - - - -
3 p - p - - - - -
2 - K - - - - - -
1 - - - - - - - -
a b c d e f g h
8 - - - - - - - -
7 - - - - - - k -
6 - - - - - - - -
5 - - - - - - - -
4 p p - - - - - -
3 p - - - - - - -
2 - K - - - - - -
1 - - - - - - - -
a b c d e f g h
8 - - - - - - - -
7 - - - - - - k -
6 - - - - - - - -
5 - - - - - - - -
4 - p p p - - - -
3 - - p - - - - -
2 - K - - - - - -
1 - - - - - - - -
a b c d e f g h
-- Michael Niermann <michael@emmy.mathematik.uni-dortmund.de>
I talked to Zek on ICS, and he mentioned that he had found solutions
for 5-8 pawns; I took this as a challenge and quickly found this
family of solutions for 3-7:
8 - - - - - - - - 8 - - - - - - - -
7 p p - - - - k - 7 - - - - - p k p
6 p - - - - - - - 6 - - - - - - - p
5 - - - - - - - - 5 - - - - - - - p
4 - - - - - - - - 4 - - - - - - - -
3 - - - - - - - - 3 - - - - - - - -
2 - K - - - - - - 2 - K - - - - - -
1 - - - - - - - - 1 - - - - - - - -
a b c d e f g h a b c d e f g h
8 - - - - - - - - 8 - - - - - - - -
7 - - - - p - k p 7 - - - p - - k p
6 - - - - - - - p 6 - - - - - - - p
5 - - - - - - - p 5 - - - - - - - p
4 - - - - - - - p 4 - - - - - - - p
3 - - - - - - - - 3 - - - - - - - p
2 - K - - - - - - 2 - K - - - - - -
1 - - - - - - - - 1 - - - - - - - -
a b c d e f g h a b c d e f g h
8 - - - - - - - -
7 - - p - - - k p
6 - - - - - - - p
5 - - - - - - - p
4 - - - - - - - p
3 - - - - - - - p
2 - K - - - - - p
1 - - - - - - - -
a b c d e f g h
The solution for 7 almost doesn't work, as 15 captures are required if
the c7 pawn is removed. This observation led me to this solution for
8 pawns:
8 - - - - - - - -
7 p - - - - - k p
6 p - - - - - - p
5 - - - - - - - p
4 - - - - - - - p
3 - - - - - - - p
2 - K - - - - - p
1 - - - - - - - -
a b c d e f g h
This works as 16 captures are required if no pawn is removed and <16 if
any pawn is removed.
-- Chris Long <clong@cnj.digex.net>