This picture illustrates that there are 512 different ways to color a 3x3 grid using only two colors.
In general, to do this for a MxM grid with M2=N blocks, there are 2N different ways.
This is also equivalent to the following:
- 2N is the sum of all the numbers in the Nth row of Pascal’s triangle.
- For a set S with N elements, 2N is the size of the power set of S, which is how many unique subsets there are of S.
- 2N is the number of ways of choosing 0 things from N things, plus the number of ways of choosing 1 thing from N things, plus the number of ways from choosing 2 things from N things, etc… , plus the number of ways of choosing N things from N.
- 2N is the number of different sequences of outcomes from flipping a coin N times.
- 2N is the number of basis states needed to completely express the state of a quantum computer with N qubits (cf. here).
Can you think of anymore?
(via wowgreat)
