# Illegal Cluster - Circe

BigDoggProblem
Posers and Puzzles 14 Sep '06 19:36
1. BigDoggProblem
Court Jester
14 Sep '06 19:361 edit
Illegal Cluster A position that becomes legal when any piece (except a King) is removed.

Circe Captured pieces immediately 're-birth' on their home square. Pawns rebirth on the file of capture; Rooks, Knights and Bishops on the home square of the same color as the capture square. For example, a White Rook captured on d5 rebirths on h1; a White Knight captured on g3 rebirths on g1, etc.

Circe
Add a White K, Q and Black K, P, B to form an Illegal Cluster
2. 15 Sep '06 10:171 edit
Maybe like this?

This position is illegal because before Qh5+ black has no last move (the only possible last move is a capture on b5, but then where is the captured piece?).
It is clear why removing the bB, bP or wQ makes the position legal.
Without the wB the position is legal because the last moves were 1...KxQb5 [+wQd1] 2.Qh5+. Without the wP the position is legal because the last moves were 1...KxRb5 (the rook isn't reborn because the wQ is on h1) 2.Qh1-h5+.
3. BigDoggProblem
Court Jester
15 Sep '06 16:52
Originally posted by David113
Maybe like this?

[fen]8/1p6/b7/1k5Q/8/3K4/4B2P/8[/fen]

This position is illegal because before Qh5+ black has no last move (the only possible last move is a capture on b5, but then where is the captured piece?).
It is clear why removing the bB, bP or wQ makes the position legal.
Without the wB the position is legal because the last moves were 1...Kx ...[text shortened]... ecause the last moves were 1...KxRb5 (the rook isn't reborn because the wQ is on h1) 2.Qh1-h5+.
Very good. Few people were able to solve this one! It was entered in a live solving tournament, and only GM solver Michel Caillaud got the solution, albeit after time expired.