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That's true. But my assumption was that the author allows a second move for a given neighbor whereby he has to move up/down, side/side from the spot he acquired after the first move. - Foolman


I wan't disputing the assumption that a second move is allowed. Moving twice is certainly mandatory for one guy since everyone has to move at least once and there is an odd number.

It is just that in the end result, one guy ends up in a spot that is not adjacent to his original starting position; but rather diagonal to it and the problem states he isn't jealous of diagonal squares.
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