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UKMT Junior Mathematical Challenge, 2019

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The diagram shows the first fifteen positive integers arranged in a 'triangle'. These numbers are to be rearranged so that the five integers along each 'edge' of the triangle have the same sum, unlike the example shown. When this is done, what is the greatest possible such sum?

(A) $38$ (B) $42$ (C) $48$ (D) $52$ (E) $54$

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