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Spanning trees of a two-dimensional n-by-n grid graph

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In-place perfect shuffle permutation

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Keep splitting

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The total number of squares on a chessboard

Given a graph G constructed from a two-dimensional n-by-n grid, what is the number of spanning trees of G?

Define the perfect shuffle permutation of order n to be the permutation:

i -> 2*i mod (n+1), i = 1,2, ..., n

where n is an even number.

1. A pile of 1000 stones, split it to two piles x and y, you get a number xy. Split x and y further, you a number for each of ...

Tags: brainteaser

Determine the total number of squares of all sizes and positions on an ordinary 8x8 chessboard. Also compute the total number of rectangles.

Tags: geometry combinatorics