Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Number problems at primary level that require careful consideration.
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
Can you substitute numbers for the letters in these sums?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using 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!
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
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!
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
This challenge is about finding the difference between numbers which have the same tens digit.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Can you find all the ways to get 15 at the top of this triangle of numbers?
This task follows on from Build it Up and takes the ideas into three dimensions!
What happens when you round these three-digit numbers to the nearest 100?
What two-digit numbers can you make with these two dice? What can't you make?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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?
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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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.
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
My briefcase has a three-number combination lock, but I have
forgotten the combination. I remember that there's a 3, a 5 and an
8. How many possible combinations are there to try?
Can you find the chosen number from the grid using the clues?
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
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?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
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?
Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?
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 these head, body and leg pieces to make Robot Monsters which are different heights.
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
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?
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?