Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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 a train the same length as Laura's but using three
differently coloured rods? Is there only one way of doing it?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
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?
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
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?
If you hang two weights on one side of this balance, in how many
different ways can you hang three weights on the other side for it
to be balanced?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you substitute numbers for the letters in these sums?
Can you put the 25 coloured tiles into the 5 x 5 square so that no
column, no row and no diagonal line have tiles of the same colour
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?
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?
A game for 2 people. Take turns placing a counter on the star. You
win when you have completed a line of 3 in your colour.
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.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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!
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
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!
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
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?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Ben has five coins in his pocket. How much money might he have?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Can you find the chosen number from the grid using the clues?
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.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
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?
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
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.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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.
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?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you use the information to find out which cards I have used?
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.