### Consecutive Numbers

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

### 14 Divisors

What is the smallest number with exactly 14 divisors?

### 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?

# To Run or Not to Run?

##### Stage: 3 Short Challenge Level:

Let the athlete take x minutes to cycle one mile.

Therefore he takes 3x/2 minutes to run one mile and 3x minutes to walk one mile.

Therefore 3x +3x/2 +x = 3x + 10 i.e. x = 4 The cyclist takes 12 minutes to walk the first mile, 6 minutes to run the second mile and 4 minutes to cycle the third mile, a total time of 22 minutes.

This problem is taken from the UKMT Mathematical Challenges.
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