NRICH provides thousands of free online mathematics resources for ages 3 to 18, covering all stages of early years, primary and secondary school education – completely free and available to all.

25 of the storeys of a 50 storey building are painted gold, and the rest are painted black…

The sum of five consecutive integers is equal to the sum of the next three consecutive integers. Can you find the largest of these integers?

These are the results when 3 numbers were added in pairs. What were the numbers?

Three numbers add up to 100. The difference between the larger two is 12 and the difference between the smaller two is 2. What are the numbers?

Amy misread a question and got an incorrect answer. What should the answer have be?

 How much money did the pensioner have before being robbed?

Can you find the volume of a cuboid, given its perimeters?

Can you work out how many members this choir has from these percentages?

Brian chooses an integer and operates on it. Work out the largest integer that he could have chosen.

Find a factor of 248−1.

The area of a rectangle is 225 square units. Find its width.

Can you put these products in order of size?

Find the shortcut to do this calculation quickly!

What are the possible lengths for the third side of this right-angled triangle?

Jane accidentally multiplied by 54 instead of 45, and her answer was 198 too big. What number did she multiply 54 by?

Can you work out what fraction of this grid is shaded?

This tiled floor has 109 purple tiles. How many tiles are there altogether?

How many diagonals does a regular icosagon (20 sides) have?

When will 2000 appear in this sequence?