Problems of the past month – did you see the solutions?

April Swindles by Pal Benko

On the first of April Pal Benko, the world-famous GM and problem composer, one to the greatest in the field, sent us a number of humorous problems. He called his piece "April Swindles", and if you missed it you can try solving them here. The solutions are given below the problems themselves. The first two represent the numbers 8 and 8, and stand for the age of the composer.

Problem 1: For both positions the question is: how many mates are there for White in one move. The first problem is for kids, the second one is for adults – it needs some thought. In both cases: what was the last move, before the diagram?

Problem 2a: On how many squares can you put the black king so that White can mate in one move. And Problem 2b: Where can you put the black king so it is White to play and mate in two? We found these two problems unexpectedly difficult.

Problem 3: On how many squares can you place the white queen, so that, with Black to play, he can mate in one move, in two different ways?

Problem 4a: White to play, helpmate in three (i.e. both sides cooperate to get Black mated in three moves). Problem 4b: Second solution, White to play, helpmate in three. Here you have to consider the previous move by Black.

Problem 5a: Black to play, White checkmates all ten black kings, simultaneously, in two moves. Problem 5b: White to play, checkmates all ten black kings, simultaneously, in three moves.

The solutions to problem 5 cannot be easily displayed on our JavaScript PGN player, which worries about "legality" or something like that. The solutions are:

1.K8d7 Bb5+ 2. Kdd6 Ne6#
1.b8N! Kdc8 2. Ba6+ K8d8 3. Ne6#!

All ten black kings are checkmated (problem 5b)

Solutions to the other problems

The Illescas Challenge

In an article entitled "On human and computer intelligence in chess" we presented the reaction of Miguel Illescas, a top Spanish GM and trained computer scientist, to a chess position published by famous mathematics professor Sir Roger Penrose. Miguel included a challenge:

Our readers were invited to analyse the above position, here on our news page, or with their favourite chess engine, to solve it with machine assistance. A number did, and in fact provided interesting feedback on the fortress theme. Here is the solution as provided by Miguel Illescas:

The solutions to the Nihal Sarin problems will follow soon!