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Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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14 Divisors

What is the smallest number with exactly 14 divisors?

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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?

Magician's Hat

Stage: 2 and 3 Short Challenge Level: Challenge Level:2 Challenge Level:2
Kan must know for sure that Roo's cards are either both even or both odd. The only way he can be sure of this is if he's selected the three even cards leaving Roo only odd numbered cards. Therefore Kan has cards $2$, $4$ and $6$ and the sum of his cards is $12$.

This problem is taken from the UKMT Mathematical Challenges.
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