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UKMT Hamilton Olympiad, 2018

Number theory Difficulty 2.0 Junior Prove it United Kingdom

The figure shows seven circles joined by three straight lines. The numbers 9, 12, 18, 24, 36, 48 and 96 are to be placed into the circles, one in each, so that the product of the three numbers on each of the three lines is the same. Which of the numbers could go in the centre?

Figure for this problem

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