Using the numbers 1, 2, 3, 4 and 5 once and only once, and the
operations x and ÷ once and only once, what is the smallest
whole number you can make?
All the girls would like a puzzle each for Christmas and all the
boys would like a book each. Solve the riddle to find out how many
puzzles and books Santa left.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
This problem is designed to help children to learn, and to use, the two and three times tables.
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
56 406 is the product of two consecutive numbers. What are these
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
Can you work out what a ziffle is on the planet Zargon?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
If the answer's 2010, what could the question be?
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
Choose a symbol to put into the number sentence.
Use the information to work out how many gifts there are in each
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
There are four equal weights on one side of the scale and an apple
on the other side. What can you say that is true about the apple
and the weights from the picture?
Number problems at primary level that require careful consideration.
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. . . .
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
This number has 903 digits. What is the sum of all 903 digits?
Number problems at primary level that may require determination.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
What is happening at each box in these machines?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Can you arrange 5 different digits (from 0 - 9) in the cross in the