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Phénix

No. 106, April 2002 - SOLUTIONS

3943 - A. Buchanan


3944 - A. Buchanan


3945 - P. Wassong


3946 - M. Caillaud


3947 - T. le Gleuher


3948 - M. Caillaud

Solution provided by Mark J. Tilford <tilford(at)ugcs.caltech.edu>:

(Note: I use WWB to refer to "White's Bishop that travels on White Squares", or "White's White Bishop". I find this term more useful than "White's King's Bishop".)

The BK is in check from the WB, and the only way to administer is via promotion. (i)

WPg3 came from H2 (1 cap), WPf4 came from E2 (1 cap), WPC3 from B2 (1 cap), so the promotee is from A2, and directly came from F7 (the only square it could reach) (5 cap). That totals 8 captures, and accounts for all missing black pieces. (ii)

BPe6 came from D7 (or it would have blocked A2), BPc4 came from A7. (iii)

BBg8 couldn't have arrived there after the WP promoted to WB (no time), or while WP was on F7 (blocked by F7 & H7), so it arrived before the WP reached F7. BPd7 captured after WP reached F7 (or it would have blocked the pawn), and BBc7 was trapped until BPd7 captured. Therefore, BBg8 isn't the original bishop; it is promoted. (iv)

The BWB isn't on the board now, so it was captured in one of the moves listed in (ii). It wasn't taken by A2 (by iv, it was trapped until after all those captures occurred), and it wasn't taken by B2 or H2 (those captures were on black squares). Therefore, it was captured by E2 on F3. (v)

BBg8 didn't promote on H1 (it couldn't get off), D1 or F1 (it was blocked by C2, G2, and E2 (which didn't capture until after the BB reached g8 (iv&v). It promoted on a white square, so it promoted on B1. G7 couldn't have reached B1 (it was blocked by C2 & B2/C3), so BPf7 promoted. F7 needs 4 caps, A7 needs 2, and D7 needs 1. That accounts for all 7 captures by black. (vi)

The BPg7 therefore didn't promote, and so was captured by one of the moves in (ii). Since it didn't capture (vi), it was taken on g3. (vii)

BBB wasn't taken by A2 (all those captures were on white squares), or E2 or H2 (their captures are accounted for), so it was taken by B2 on c3. (viii)

WBB was captured by one of the moves in (vi), and wasn't taken by D7 or F7 (those captures were on white squares), so it was captured by A7. (ix)

WWB was captured by a move in (vi). It was trapped until after E2xBWB, which is after D7 and F7 made all their captures. The only remaining move is that it was taken by A7. (x)

Since A7 took WBB and WWB, it made one capture on a black square, and one on a white square. The only way to do this is A7xWBB on A7, and A5xWWB on C4. (xi)

(Also, B2 must have captured BBB before BPf7 could promote, so it is possible to tell what order the bishops were captured in

In short, in order