Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

What happens when you round these three-digit numbers to the nearest 100?

What happens when you round these numbers to the nearest whole number?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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

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!

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.

Find the values of the nine letters in the sum: FOOT + BALL = GAME

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

Can you replace the letters with numbers? Is there only one solution in each case?

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

Have a go at balancing this equation. Can you find different ways of doing it?

Can you work out some different ways to balance this equation?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

Can you find all the ways to get 15 at the top of this triangle of numbers?

This task follows on from Build it Up and takes the ideas into three dimensions!

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

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?

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?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

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.

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?