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Programming Enigma Puzzles

14 February 2020

Posted by on **From New Scientist #2128, 4th April 1998** [link]

The game of choss is played by two players, Black and White, on a board of 6 × 6 squares. Each player has a number of pieces which he or she moves one square horizontally or vertically. The players take it in turns to move one of their own pieces. A piece cannot move into a square already occupied by a piece of the same colour. If a piece moves into a square occupied by a piece of the opposite colour, that the other piece is captured and removed from the board. One White piece is larger than the other pieces and is called the Target. Black wins by taking the Target.

The layout of the board is as shown and it is Black’s move. She can in fact definitely win in three or fewer moves.

1. What should the first of these moves be?

That was the Enigma that I intended to set, but the editor thought it was too easy. He suggested that I change the board layout above by moving the Target to some other unoccupied square where it cannot be immediately taken by Black, but so that from the new layout Black can again definitely win in three or fewer moves. He then suggested that I asked Question 1 about this new layout.

Of course I shall have to choose the new position of the Target so that Question 1 has a unique answer.

2. To which position should I move the Target?

[enigma973]

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This Python program examines moves for black such that whatever response white makes black is guaranteed a win in three moves.

To analyse all the situations required by the puzzle text takes it 900ms.

Run:[ @repl.it ]Solution:(1) Black’s first move should be d5 → e5. (2) The Target should be placed at d2.For (2), if black moves d4 → d3, then they guarantee a win in three moves.

If the Target were placed at c2, then black could still guarantee a win in three moves, but there are two options for the initial move (b1 → b2, or: b3 → b2), so this is ruled out as a solution, as we require a single initial move for black.