Proof games with 3 solutions
11 Feb. 2011 | by Peter Wong
In a proof game problem, the aim is to reconstruct the game that leads to the diagram position (from the normal opening array), using the fewest possible moves. By convention, the solution of a PG will consist of a precise sequence of moves, without any dual or alternative move order. Because of this requirement, it’s fairly difficult to compose a PG problem with two precise solutions, where both arrive at the same final position. A PG that involves three solutions, then, would be particularly challenging to set up, and the first problem to achieve this task is given below.
Problem Observer 1995, 1st Prize
Proof game in 6½, 3 solutions
Its stipulation of “PG in 6½” means that the diagram has to be reached after White’s 7th move. The theme shown is a three-fold change of white “raiders”, or pieces that capture various enemy units before returning to their home squares.
This problem of mine was mentioned in Part II of Mark Kirtley’s ‘Proof Games Shorties’, a series of articles on PGs that are at most seven moves in length. The author of the article asked if anyone knew of, or could create, another PG with three solutions. This challenge was not met until a few years later, when in Part V of the series (which for some reason is not included on the Retrograde Analysis Corner site linked above) another problem with the same task was uncovered.
Proof game in 7, 3 solutions
This marvellous work by Göran Wicklund has three quite varied solutions, one of which is especially surprising by diverging from the symmetrical play seen in the other two parts. I am withholding the solutions to both PGs to encourage you to solve them!