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

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

Four Kinds of Fruits

p e a r
a p p l e
l e m o n
+ b a n a n a
= o r a n g e

IBM ponder 09/2008

Consider a 13x13 checkerboard. It can be partitioned into a collection of
smaller square checkerboards in various ways. For example into 169 1x1
checkerboards or into 1 12x12 and 25 ...

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Passengers on an airplane

An airplane has n seats, and all of them have been sold for a particular flight, with no overbooking. When the last passenger arrives, he finds that his seat is ...

Truck moving around a circle of gas stations

you have a truck that is moving around a circular track with gas stations spaced out at some distance between them. Each station has a finite amount of gas, the ...