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Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Weekly Problem 52 - 2009

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

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?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

 

 

This problem is taken from the UKMT Mathematical Challenges.

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