Jealous Neighbors
From Car Talk
JEALOUS NEIGHBORS
RAY: This week's Puzzler was sent to me from Bruce Robinson, a professor of civil and environmental engineering at the University of Tennessee. It goes like this: There are 25 jealous people who live in the squares of a five-by-five grid. We're gonna number the squares, starting in the upper left-hand corner, 1 through 25.
TOM: So the first row starts with 1, the second row starts with 6, the third row starts with 11, and so forth.
RAY: Right. Remember, each person is jealous of his adjacent neighbor. Not his diagonal neighbor, but the person up or down or left or right of him. Each aspires to move into the apartment of his adjacent neighbor.
The question is very simple: What is the fewest number of total moves that can accomplish this?
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