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Problem

In the diagram below, the number on the connecting line is the sum of the two numbers in the circles.

What numbers are missing from the circles in the diagram below?

Solution

By labelling each vertex as follows.

a + b = 13, b + c = 25 and a + c = 20.

Adding all three equations, 2a + 2b + 2c = 58 a + b + c = 29

As a + b = 13, we get 13 + c = 29 c = 16

Similarly, b + 20 = 29 b = 9 and a + 25 = 29 a = 4