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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. . . .
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?
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. . . .
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.
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?
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. . . .
Find the values of the nine letters in the sum: FOOT + BALL = GAME
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
What is the sum of all the digits in all the integers from one to one million?
This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.
This article suggests some ways of making sense of calculations involving positive and negative numbers.
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?
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?
Find the numbers in this sum
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
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?
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. . . .
What is the sum of all the three digit whole numbers?
There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?
Find a great variety of ways of asking questions which make 8.
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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?
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.
The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre jug is full of wine, the others are empty. Can you divide the wine into three equal quantities?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
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?
Using the 8 dominoes make a square where each of the columns and rows adds up to 8
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
This number has 903 digits. What is the sum of all 903 digits?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
How can we help students make sense of addition and subtraction of negative numbers?
There are nasty versions of this dice game but we'll start with the nice ones...
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
What is happening at each box in these machines?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
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?
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
You have 5 darts and your target score is 44. How many different ways could you score 44?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?