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Gar the Magician wrote each of the numbers from $1$ to $7$, one on each of seven cards, and placed them in his hat. He offered the hat to two other magicians, Kan and Roo. Kan took, at random, $3$ cards from the hat and Roo took $2$ cards (so that there were $2$ cards left in the hat). Kan told Roo: "I can deduce that the sum of the numbers of your cards is even". What was the sum of the
numbers on Kan's cards?
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This problem is taken from the UKMT Mathematical Challenges.
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