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There are six squares to be guarded by the five remaining pieces, so one piece guards two squares while the others each guard one. Since there's no way for an unobstructed rook to guard less than three squares it needs to be blocked by a second piece standing next to the black King. That still leaves a lot of possible stalemate positions, but in order to allow ten checkmates on the previous move it will be necessary to arrange it so that the blocking piece can discover check from the rook. The bishop is the best choice for the blocking piece (since it can hold a guard on one square while moving), which forces Rook on h5 and Bishop on g5. The only way to guard g6 now is with the Knight on h8. This leaves e6 and g4 to be guarded by the Pawn and Queen. If we place the Pawn on d5 the Queen must be placed on d1, and a little experimentation will show there's no way to retract a move to allow ten checkmates. With the Pawn on h3 the Queen can stand on a2, b3, or c4. Each of these allow the Queen access to the sixth rank (an excellent location for maximizing mates), but only from c4 can the Queen reach the optimal sixth-rank square, namely c6.

(The blue spot shows were Blanc moved the Queen and the red spots show the possible checkmates if he had not made the blunder.)


However, solvers took a slightly different approach in solving this puzzle and came up with a different board. The Bishop could also be placed on d1.

(The blue spot shows were Blanc moved the King and the red spots show the possible checkmate if he had not made the blunders.)
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