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MYTS 2019 - Grade 7 - Round 2 Question 4

MYTS · MYTS 2019 - Grade 7 - Round 2

Question 4

There are 50 cards, each labelled with a positive integer at most 50, with distinct labels on different cards. Does there exist a positive integer $n$ such that all 50 cards can be placed in $n$ boxes, and in every box the cards can be split into two groups whose label sums are equal?

For a group containing only one card, its sum means that card’s label.

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