The puzzle (this may have a known answer) is to construct a position such that:
- If Black makes move A, it's mate in 1 for white.
- If Black makes move B, it's mate in 2 for white.
- If Black makes move X, it's mate in N for white.
For instance, in this position
6k1/7p/5K1P/8/8/4Q3/8/8 b - - 0 1
- If 1..Kh8 2. Qe8#
- If 1..Kf8 2. Kh8 Qe8#
So this position has N=2.
What's the highest possible N? (All of the 1-N moves must exist)
- It doesn't count as having mate-in-X if white also has a shorter forced mate.
- It is acceptable for white to have several different mate-in-X for a given black response.
- It is acceptable for black to have additional moves available that don't lead to any particular mate-in-X.
- It is acceptable for black to have two different moves that both forced mate in the same number of moves.
(It might be considered "nicer" to have solutions that don't rely on the last three points though).