Rectangle Paths

Probability Level 5

A 2×132 \times 13 rectangle is divided into unit squares. You must write the numbers 1 through 2626 into these unit squares, and satisfy the following criteria.

1) Each number is in a different square.

2) The number 1 must be in a corner.

3) The numbers ii and i+1i+1 must share an edge (of a unit square), for 1i251 \leq i \leq 25.

How many different ways can you write the numbers into the squares?

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