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IMSO 2009 Mathematics – Taiwan Selection – Exploration Question 3

IMSO Maths · IMSO 2009 Mathematics – Taiwan Selection – Exploration

Question 3

The diagram represents a small sheet of 12 postage stamps, all perforated at their edges and all of the same value. The letters only identify the stamps.

Question illustration

You need 4 stamps to post a letter and want all 4 properly joined together at their edges, not merely at corners. For example, ABCD, EFGH, JKLM and FGHL work, but EFLM does not. In how many different ways can you obtain such a group of 4? Write down this number.