(Inspired by this cool problem)
Let’s say it’s White to move. Let A = the number of squares currently attacked by White, and B = the number of squares attacked by White after White’s next move.
What is the maximum possible value of B - A?
A “attacked” square’s definition is just as you’d expect. More rigorously, a square is attacked by White if, after Black skips the next move, a White piece can legally capture anything on that square. Specifically, if it were empty, then after teleporting a dummy black piece onto that square, a White piece must be able to legally capture that dummy piece. (A dummy piece does not attack). If it were occupied by a white piece, then it must be legally defended by another white piece (the sequence “black captures the white piece with a dummy black piece, and white recaptures the dummy piece with some white piece” must be legal). If it were occupied by a black piece, it must be able to be legally captured by a white piece.
For example, in the linked problem above, we have A = 26 and B = 58. This means B - A = 32, which is really high. But is this the best we can do?
Another example: after opening moves
1. e4 c5 2. Bc4 a6 3. Nf3 we note that Black’s c-pawn attacks
d4, but he does not attack
f7, because the King cannot move into check. Furthermore, after a random move (say
3. … h6),
f5 is attacked by White’s e-pawn.
In the solution, preferably, the “current position” should be legal, but if there’s a really nice illegal solution we should see it too.