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?

Rule of Three

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

Weekly Problem 25 - 2010

Stage: 3 Short Challenge Level:

Four touching circles all have radius 1 and their centres are at the corners of a square.
What is the radius of the circle through the points of contact $X, Y, Z$ and $T$?

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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