What is the maximum number of checked squares on a board that delivers checkmate without a draw?

Question

I’ve long dreamt of delivering a “super checkmate”.

Imagine that as his dying wish, when in checkmate, the king can magically transport himself to any open square on the board.

What is the board configuration which minimizes the number of squares he can safely teleport to? Is it possible for there to be no safe squares, so the king’s wish can’t save him?

Of course, we can imagine somehow the opponent promoted all his pawns to queens along the back rank, so every square is covered, but this configuration is not achievable without having drawn along the way (I believe; but prove me wrong!).

So I’m looking for a practical configuration that can be achieved naturally where the last move is checkmate.

Bonus points for each square that is under attack more than once.

Answer 1

Any position with roaming kings is hardly "natural," so I believe you mean if such a position is legal. If I understand correctly, kings may only attempt teleportation if checkmated; otherwise, it would be nigh impossible to checkmate.

Firstly, it is possible to promote eight queens and checkmate without drawing.

[FEN "8/PPPPPPPP/8/8/8/K7/8/1k6 w - - 0 1"]

1. c8=Q Ka1 2. a8=Q Kb1 3. d8=Q Ka1 4. e8=Q Kb1 5. f8=Q Ka1 6. h8=Q Kb1 7. b8=Q+ Ka1 8. g8=Q#

This effect may also be achieved by utilizing White's eight officers. I recall this problem by Josef Kling. The stipulation is "White checkmates in 14 moves but only after attacking all 64 squares." I would suppose that this position is more "natural" than one with eight queens.

[Title "Josef Kling, The Chess Player's Companion 1849, 'Fancy Sketch'"]
[FEN "4k3/8/8/8/8/8/8/RNBQKBNR w - - 0 1"]

1. Qd6 Kf7 2. Rh8 Kg7 3. Bb2+ Kf7 4. Qa6 Ke7 5. Bh3 Kf7 6. Ke2 Ke7 7. Kd3 Kf7 8. Bd4 Ke7 9. Nd2 Kf7 10. Ne2 Ke7 11. Rg1 Kf7 12. Nc3 Ke7 13. Nd5+ Kf7 14. Be6# 

(On a technical note, only 63 squares can actually be attacked and one occupied, but Kling knew this and 64 sounds better on paper. I also presume kings cannot teleport to occupied squares.)