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

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.

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?

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.

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.

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

This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.

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?

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

Whenever two chameleons of different colours meet they change colour to the third colour. Describe the shortest sequence of meetings in which all the chameleons change to green if you start with 12. . . .

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

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

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

There are exactly 3 ways to add 4 odd numbers to get 10. Find all the ways of adding 8 odd numbers to get 20. To be sure of getting all the solutions you will need to be systematic. What about. . . .

This Sudoku, based on differences. Using the one clue number can you find the solution?

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. . . .

Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.

Find a great variety of ways of asking questions which make 8.

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

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?

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?

Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was. . . .

How can we help students make sense of addition and subtraction of negative numbers?

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?

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

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

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.

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.

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.

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

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

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

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?

Number problems at primary level that require careful consideration.

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?

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

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

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

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

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?

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.