There were 22 legs creeping across the web. How many flies? How many spiders?
Claire thinks she has the most sports cards in her album. "I have
12 pages with 2 cards on each page", says Claire. Ross counts his
cards. "No! I have 3 cards on each of my pages and there are. . . .
Woof is a big dog. Yap is a little dog.
Emma has 16 dog biscuits to give to the two dogs.
She gave Woof 4 more biscuits than Yap.
How many biscuits did each dog get?
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
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 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.
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?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
In this problem you have to place four by four magic squares on the
faces of a cube so that along each edge of the cube the numbers
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?
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
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?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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.
Fill in the numbers to make the sum of each row, column and
diagonal equal to 15.
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?
On Planet Plex, there are only 6 hours in the day. Can you answer
these questions about how Arog the Alien spends his day?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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.
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 the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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 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!
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
This challenge is about finding the difference between numbers which have the same tens digit.
Can you arrange 5 different digits (from 0 - 9) in the cross in 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!
Can you find 2 butterflies to go on each flower so that the numbers
on each pair of butterflies adds to the same number as the one on
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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!
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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?
A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Number problems at primary level that may require determination.