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?

Painted Purple

Stage: 3 Short Challenge Level:

A wooden cube has three of its faces painted red and the other three of its faces painted blue, so that opposite faces have different colours. It is then cut into $27$ identical smaller cubes. How many of these new cubes have at least one face of each colour?

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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