Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . .
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Replace each letter with a digit to make this addition correct.
Got It game for an adult and child. How can you play so that you know you will always win?
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. . . .
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 sum of all three-digit numbers each of whose digits is odd.
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?
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. . . .
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.
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.
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.
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.
I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?
By selecting digits for an addition grid, what targets can you make?
Can you find different ways of creating paths using these paving slabs?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Try out some calculations. Are you surprised by the results?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
In this simulation of a balance, you can drag numbers and parts of number sentences on to the trays. Have a play!
Number problems at primary level that may require resilience.
Try out this number trick. What happens with different starting numbers? What do you notice?
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.
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?
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?
Number problems at primary level to work on with others.
This Sudoku, based on differences. Using the one clue number can you find the solution?
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?
This Sudoku requires you to do some working backwards before working forwards.
What happens when you add a three digit number to its reverse?
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?
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.
Choose a symbol to put into the number sentence.
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
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 score 100 by throwing rings on this board? Is there more than way to do it?
Can you substitute numbers for the letters in these sums?
What is happening at each box in these machines?
If the answer's 2010, what could the question be?
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!
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?
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?