Delight your friends with this cunning trick! Can you explain how it works?

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

This article suggests some ways of making sense of calculations involving positive and negative numbers.

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

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

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?

Use the information to work out how many gifts there are in each pile.

Find out about Magic Squares in this article written for students. Why are they magic?!

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

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?

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.

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

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

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to. . . .

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?

Max and Mandy put their number lines together to make a graph. How far had each of them moved along and up from 0 to get the counter to the place marked?

In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.

If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?

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?

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?

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat. . . .

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

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

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?

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?