What is the longest fixed sequence of consecutive moves you can find in any legal position that
- guarantees checkmating the opponent regardless of their responses (whether by forcing particular responses or otherwise), AND
- is the shortest available fixed sequence of consecutive moves that checkmates the opponent in that position?
Have a look at the position below:
[White "Checkmater"] [Black "Checkmatee"] [FEN "r5r1/1pq1k1Bp/3pb1p1/1p1P1p2/8/5N2/PP2QPPP/R3K2R w - - 1 18"] 1.Qxe6+ Kd8 2. Bf6+ Qe7 3. Qxe7+ Kc8 4. Rc1+ Kb8 5. Qc7+ Ka7 6. Bd4+ Ka6 7. Qb6#
In theory White has M5: 1.Qxe6+ Kd8 2.Bf6+ Qe7 3.Bxe7+ Ke8 (3...Kc7 4.Qxd6+ Kc8 5.Rc1#) 4.Bf6+ Kf8 5.Qe7#. But White's third move has to be different to achieve these mates: no one move works in both cases of 2...Ke8 and 2...Kc7. (For example, try 3.Bxd6+: with this, 2...Ke8 3.Bxd6+ comes with M2, and 2...Kc7 3.Bxd6+ comes with M5, yet neither of the two mates can be achieved by a fixed sequence of moves.)
However, White has the fixed sequence of moves shown above which guarantees checkmate (satisfying condition 1): 1.Qxe6+ Kd8 2.Bf6+ Qe7 3.Qxe7+ Kc8 4.Rc1+ Kb8 5.Qc7+ Ka7 6.Bd4+ Ka6 7.Qb6#. At 7 checkmater moves long this also appears to be the shortest fixed sequence available in the position above which guarantees checkmate (satisfying condition 2) - for example, we can create longer but equally forced sequences that also satisfy condition 1, such as trivially extending the mate above for example with 3.Qxe7+ Kc8 4.Rc1+ Kb8 5.Qc7+ Ka7 and now instead of 5.Bd4+, play e.g., 5.Qa5+ Kb8 6.Qc7+ Ka7, etc., and thereby add a few moves to lengthen the sequence while keeping it fixed and mate certain at the end.
Note that there is no necessity (in principle at least) for the opponent's moves to be forced. Condition 1 is satisfied as long as - no matter what Black chooses, if they have any choice - the same continuation for White (the checkmater) still results in checkmate.
Above I showed a position where the shortest fixed consecutive series of moves by White that guarantees checkmating Black is 7 moves long. (Not that I claim this as any kind of record.) I would like to see positions where there exists a sequence that satisfies these criteria and where that sequence is as long as possible - I'm guessing 8,9 White moves is small fry for some of the people here.