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!
Find the sum of all three-digit numbers each of whose digits is
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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?
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 do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
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?
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
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?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
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?
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?
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.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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.
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
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?
This is an adding game for two players.
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
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
This challenge is about finding the difference between numbers which have the same tens digit.
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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?
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?
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!
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?
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?
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
Can you substitute numbers for the letters in these sums?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
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?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
There were 22 legs creeping across the web. How many flies? How many spiders?