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?

Colourful Tiles

Stage: 3 Short Challenge Level:

Consider the colour at the top. There are $4$ different choices for this: red, yellow, green and blue. For the right hand colour, this can be any of the other $3$ colours that have not yet been used. The bottom colour can then be either of the other $2$ colours. The left hand part then has to have the remaining colour.

This means there are $4 \times 3 \times 2 \times 1 = 24$ different ways to paint all four sections. This means there are $23$ other ways to paint the tile.

This problem is taken from the UKMT Mathematical Challenges.
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