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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?

Hiking the Hill

Stage: 3 Short Challenge Level: Challenge Level:1

Sarah goes up a hill and then down again the same way. On the way up she averages $2$ miles per hour. On the way down she averages $4$ miles per hour. What is Sarah's average speed in miles per hour for the whole journey? Give an exact answer.
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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