Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Find your way through the grid starting at 2 and following these operations. What number do you end on?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

Here is a chance to play a version of the classic Countdown Game.

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

If you have only four weights, where could you place them in order to balance this equaliser?

Can you hang weights in the right place to make the equaliser balance?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

Find all the numbers that can be made by adding the dots on two dice.

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

Use these head, body and leg pieces to make Robot Monsters which are different heights.

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!