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UKMT Grey Kangaroo, 2016

Combinatorics Difficulty 2.0 Junior Find the answer United Kingdom

The cube shown is divided into $64$ small cubes. Exactly one of the cubes is grey, as shown in the diagram. Two cubes are said to be 'neighbours' if they have a common face. On the first day, the white neighbours of the grey cube are changed to grey. On the second day, the white neighbours of all the grey cubes are changed to grey. How many grey cubes are there at the end of the second day?

(A) $11$ (B) $13$ (C) $15$ (D) $16$ (E) $17$

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