Blue squares indicate the last move made by Black. It is White's turn now. Which is the best move for White?
Clarifications
:
White pawn starts from column 2.
Black pawn starts from column 7.
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We can see that white king movement is restricted to row 1 only and both of black rook are ready to attack column 1, causing checkmate. White can not force black king to get out from g3. If both of white king and white rook do not move this turn, a black rook simply move Re8xe1#. If white king move Kg1-f1 to protect his rook, black simply Rc2-f2+, forcing king back to g1 and Re8xe1#. If white rook leaves row 1, black will move Rc2-c1+ which force white rook to block rook pathway to his king (Re1). However, the white rook does not have any protection at all, so black rook simply move Re1# (it is optional to player which black rook will move this final blow).
So the best move white can choose is simply hold his rook in row 1, preventing any black rook from reaching row 1.