Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
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.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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?
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?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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!
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?
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.
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?
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 arrange 5 different digits (from 0 - 9) in the cross in the
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?
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?
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?
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 use the information to find out which cards I have used?
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?
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 is about finding the difference between numbers which have the same tens digit.
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Can you find all the ways to get 15 at the top of this triangle of numbers?
The brown frog and green frog want to swap places without getting
wet. They can hop onto a lily pad next to them, or hop over each
other. How could they do it?
Find all the numbers that can be made by adding the dots on two dice.
This dice train has been made using specific rules. How many different trains can you make?
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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. . . .
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you substitute numbers for the letters in these sums?
Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals 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?
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.
My coat has three buttons. How many ways can you find to do up all
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.