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UKMT Grey Kangaroo, 2020

Combinatorics Difficulty 2.0 Junior Find the answer United Kingdom

Cleo builds a pyramid with identical metal spheres. Its square base is a $4 \times 4$ array of spheres, as shown in the diagram. The upper layers are a $3 \times 3$ array of spheres, a $2 \times 2$ array of spheres and a single sphere at the top. At each point of contact between two spheres, a blob of glue is placed. How many blobs of glue will Cleo place?

(A) $72$ (B) $85$ (C) $88$ (D) $92$ (E) $96$

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