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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?

Star Sum

Stage: 3 Short Challenge Level: Challenge Level:1

The ten numbers in the star total 75.

Each number appears in two "lines".

And there are five lines, making a total of 150. Which implies the total for each line is 30.

This means that R+I=24 and therefore R=11 and I = 13 (or vice versa).

If R=11 then N=12, H =10 and C=11 which is impossible.

If R=13 then N = 10; H = 12 and C= 9, which is correct.

This problem is taken from the UKMT Mathematical Challenges.

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