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Retrograde Analysis
Chess Problems

by Leo Mano

AR13 - Leo Mano
(2x5) 4k3 - 2p1P1p1 - 8 - K1p1p3 - 8 - 8 - 8 - 8

Monochromatic. No piece has ever moved from a white square to a black square and vice-versa. Which and where is the invisible piece?

Solution: Black b8.
The white e7 have captured 3 pieces. Two of these, at least, were captured on black square (one may have been captured en passant on white square). Black have four missing pieces from black squares. The missing b8 has never moved. What piece could have captured the missing b8? The white from a1 can't reach b8. The white can't reach b8 too. A white (from b2 or d2) need four captures to do it. Three of these, at least, were captured on black squares exceeding the number of missing black pieces from black squares. Remain the white .

The black on c5 came from a7 via b6. When black moved b6xc5, the white already on b4 to reach a5. Hence, there's no way to the white go to b8. The b8 was never captured and it's on the board now.

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(p)2000-2001 by Leo Mano. Rio de Janeiro - RJ, Brazil.