Two are playing the game "cats and rats" on the chess-board 8x8. The first has one piece -- a rat, the second -- several pieces -- cats. All the pieces have four available moves -- up, down, left, right -- to the neighbour field, but the rat can also escape from the board if it is on the boarder of the chess-board. If they appear on the same field -- the rat is eaten. The players move in turn, but the second can move all the cats in independent directions.
a) Let there be two cats. The rat is on the interior field. Is it possible to put the cats on such a fields on the border that they will be able to catch the rat?
b) Let there be three cats, but the rat moves twice during the first turn. Prove that the rat can escape.
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BMAD
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