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Question 12

Given a sheet of $$16$$ stamps as shown, the number of ways of choosing three connected stamps, where two adjacent stamps must have an edge in common, is

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Solution

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Counting all connected triples in the two-block stamp arrangement gives $$28$$ triples contained in the four-cell blocks, $$12$$ additional triples involving the joining region, and $$2$$ further triples crossing the central connection. Hence the total number is $$28+12+2=42$$.

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