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Consecutive Numbers

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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?

Washing-up

Stage: 3 Short Challenge Level: Challenge Level:1


A survey for washing-up liquid revealed that $\frac{2}{3}$ of all customers bought Jinx and $\frac{1}{3}$ of customers bought Kleenz. Nobody bought both. After an advertising campaign for Kleenz, the only change in sales was that $\frac{1}{4}$ of the people who had bought Jinx were now buying Kleenz instead.

What fraction of customers now buy Kleenz?


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

This problem is taken from the UKMT Mathematical Challenges.
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