A Piece of P.I.E

Probability Level 5

A 4×4 4 \times 4 square is made up of 16 1×1 1 \times 1 squares, each of which is coloured either black or white. Let nn be the number of these 4×4 4 \times 4 squares such that within the 4×4 4 \times 4 square there are no 3×3 3 \times 3 squares made up entirely of white 1×1 1 \times 1 squares. What is the digit sum of n?n?

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