No.1709 (NT&HT)

(C+ by Popeye 4.87)

A convenient set-up with this condition is the two kings mutually guarding a single square. Here we see three instances, on b2, e2 and b8. With the first two there is an extra element with black pieces occupying the squares, which has the effect of pinning the white rooks. The white knight is also pinned, but on a different line. With the key we threaten to deflect the black king, leaving White in check on e2 and b8.

On a3 the bishop defends by guarding f8 which will allow White to run to b8. The b3 rook is now free and its move gives check on b2 obliging the bishop to return. This leaves White in check on b1 which the rook moving back to b3 would cancel. But having taken the pawn, there would now be no black guard on b2, so the rook switchback is illegal.

After the black rook captures the threat piece White removes his guard of e2 again forcing a switchback.
However by capturing on c3 the rook immediately pins itself and so is unable to return to stop the mate.

It looks like the black knight is pinned, but he does have one square, d6, which doesn't result in self-check. With the threatened check on b8 now eliminated, White can nullify the check on e2 with 3.Bc4. But with its move the knight guards e8 unpinning white's knight, which proceeds to give its own check, again forcing a black switchback. Black's move now has the effect of pinning the white knight to b8, preventing it from returning to block the newly unguarded e8.

So in each case we see the Black defences unpinning a white piece which, after forcing a switchback, is itself unable to switchback to defend the mate.