The diagram shows three triangles, , and , each of which is divided up into four smaller triangles. The diagram is to be completed so that the positive integers from 1 to 10 inclusive are placed, one per small triangle, in the ten small triangles. The totals of the numbers in the three triangles , and are the same. Numbers 1, 2, 4 and 10 have already been placed.
In how many different ways can the diagram be completed?
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Junior Mathematical Olympiad 2018 (2018)
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