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Stage: 2, 3 and 4 Challenge Level:

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 do. . . .

Postage

Stage: 4 Challenge Level:

The country Sixtania prints postage stamps with only three values 6 lucres, 10 lucres and 15 lucres (where the currency is in lucres).Which values cannot be made up with combinations of these postage. . . .

Always the Same

Stage: 3 Challenge Level:

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?

Magic Squares

Stage: 4 and 5

An account of some magic squares and their properties and and how to construct them for yourself.

Connect Three

Stage: 3 and 4 Challenge Level:

Can you be the first to complete a row of three?

The Patent Solution

Stage: 3 Challenge Level:

A combination mechanism for a safe comprises thirty-two tumblers numbered from one to thirty-two in such a way that the numbers in each wheel total 132... Could you open the safe?

Eleven

Stage: 3 Challenge Level:

Replace each letter with a digit to make this addition correct.

Tis Unique

Stage: 3 Challenge Level:

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.

Aba

Stage: 3 Challenge Level:

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.

Magic Squares for Special Occasions

Stage: 3 and 4

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.

Crossed Ends

Stage: 3 Challenge Level:

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

Card Trick 2

Stage: 3 Challenge Level:

Can you explain how this card trick works?

Domino Square

Stage: 2, 3 and 4 Challenge Level:

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

Calendar Capers

Stage: 3 Challenge Level:

Choose any three by three square of dates on a calendar page...

Pyramids

Stage: 3 Challenge Level:

What are the missing numbers in the pyramids?

4 Dom

Stage: 1, 2, 3 and 4 Challenge Level:

Use these four dominoes to make a square that has the same number of dots on each side.

Clocked

Stage: 3 Challenge Level:

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?

3388

Stage: 3 Challenge Level:

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

Countdown Fractions

Stage: 3 and 4 Challenge Level:

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

Cayley

Stage: 3 Challenge Level:

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

And So on and So On

Stage: 3 Challenge Level:

If you wrote all the possible four digit numbers made by using each of the digits 2, 4, 5, 7 once, what would they add up to?

Arrange the Digits

Stage: 3 Challenge Level:

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

Pairs

Stage: 3 Challenge Level:

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. . . .

Pole Star Sudoku 2

Stage: 3 and 4 Challenge Level:

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

Constellation Sudoku

Stage: 4 and 5 Challenge Level:

Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting problem.

Cubes Within Cubes

Stage: 2 and 3 Challenge Level:

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?

As Easy as 1,2,3

Stage: 3 Challenge Level:

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

Top-heavy Pyramids

Stage: 3 Challenge Level:

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

Eight Dominoes

Stage: 2, 3 and 4 Challenge Level:

Using the 8 dominoes make a square where each of the columns and rows adds up to 8

First Connect Three

Stage: 2 and 3 Challenge Level:

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?

Twenty20

Stage: 2, 3 and 4 Challenge Level:

Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.

More Children and Plants

Stage: 2 and 3 Challenge Level:

This challenge extends the Plants investigation so now four or more children are involved.

Cunning Card Trick

Stage: 3 Challenge Level:

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

More Plant Spaces

Stage: 2 and 3 Challenge Level:

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

Make 37

Stage: 2 and 3 Challenge Level:

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.

First Connect Three for Two

Stage: 2 and 3 Challenge Level:

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.

Like Powers

Stage: 3 Challenge Level:

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.

Score

Stage: 3 Challenge Level:

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. . . .

I'm Eight

Stage: 1, 2, 3 and 4 Challenge Level:

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

Chameleons

Stage: 3 Challenge Level:

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. . . .

Got it Article

Stage: 2 and 3

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

Making Sense of Positives and Negatives

Stage: 3

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

Weights

Stage: 3 Challenge Level:

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

2010: A Year of Investigations

Stage: 1, 2 and 3

This article for teachers suggests ideas for activities built around 10 and 2010.

Stage: 3 Challenge Level:

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?

Number Pyramids

Stage: 3 Challenge Level:

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

Countdown

Stage: 2 and 3 Challenge Level:

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

Making Maths: Double-sided Magic Square

Stage: 2 and 3 Challenge Level:

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

Nice or Nasty

Stage: 2 and 3 Challenge Level:

There are nasty versions of this dice game but we'll start with the nice ones...