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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?

Intersecting Squares

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2
Three congruent squares overlap as shown.

The areas of the three overlapping sections are $2\;\mathrm{cm}^2$, $5\;\mathrm{cm}^2$ and $8\;\mathrm{cm}^2$ respectively.

The total area of the non-overlapping parts of the squares is $117\;\mathrm{cm}^2$.

What is the side length of each square?

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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