In the diagram, a number is to be written at each of the vertices of the three pentagons. Some of the numbers have already been written.
If the sum of the numbers at the vertices of each pentagon is to be
, what is the value of ?
Problem 361
Pick one
Official solution
We begin by labelling the missing numbers , , , and , as shown.
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From the pentagon on the left, we get or , and so .
From the pentagon on the right, we get or , and so .
From the middle pentagon, we get or , and so .