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# Queen game

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There is a field x on y, two players, in turn, rearrange the queen from the lower left corner to the upper right one by n cells vertically, or horizontally, or d cells diagonally (right-up). The one who cannot make a move loses. Does the player who started the game have a winning strategy?
There are four variables: x and y - the sides of the field, n - cells move vertically or horizontally, d - cells diagonally (right-up).
I tried from the end, put down + -, but the field can be 100000 by 10000000 conditionally, some algorithm for solving the problem is needed.
If anyone has ideas or an algorithm, I would be very grateful for the help.

Jul 12, 2023

#1
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Is the Queen able to move any number of squares,

as is the case on a chessboard?

If so, your winning strategy would be to move first,

then just move her all the way to the other corner.

.

Jul 13, 2023
#2
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conditions are first set, for example, the size of the field is 27 * 22 (x * y), n=3 step either up or to the right, d=4 diagonal, and so here is the winning strategy for the one who goes second

Jul 13, 2023