In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Can you substitute numbers for the letters in these sums?
Ben has five coins in his pocket. How much money might he have?
Number problems at primary level that require careful consideration.
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?
Can you make square numbers by adding two prime numbers together?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Can you use this information to work out Charlie's house number?
My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
Find all the numbers that can be made by adding the dots on two dice.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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!
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?
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
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?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Alice and Brian are snails who live on a wall and can only travel
along the cracks. Alice wants to go to see Brian. How far is the
shortest route along the cracks? Is there more than one way to go?
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.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can