Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
56 406 is the product of two consecutive numbers. What are these
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Can you work out what a ziffle is on the planet Zargon?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Imagine you were given the chance to win some money... and imagine
you had nothing to lose...
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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?
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
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?
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?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
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
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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 the information to work out how many gifts there are in each
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.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
Can you complete this jigsaw of the multiplication square?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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!
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?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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!
What is happening at each box in these machines?
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?
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?
If the answer's 2010, what could the question be?
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
What is the sum of all the three digit whole numbers?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Number problems at primary level that may require determination.
Put a number at the top of the machine and collect a number at the
bottom. What do you get? Which numbers get back to themselves?