Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Choose a symbol to put into the number sentence.
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
Imagine a pyramid which is built in square layers of small cubes.
If we number the cubes from the top, starting with 1, can you
picture which cubes are directly below this first cube?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten
numbers from the bags above so that their total is 37.
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Can you hang weights in the right place to make the equaliser
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
If you have only four weights, where could you place them in order
to balance this equaliser?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
The idea of this game is to add or subtract the two numbers on the
dice and cover the result on the grid, trying to get a line of
three. Are there some numbers that are good to aim for?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Here is a chance to play a version of the classic Countdown Game.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
We start with one yellow cube and build around it to make a 3x3x3
cube with red cubes. Then we build around that red cube with blue
cubes and so on. How many cubes of each colour have we used?
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
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
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
Can you find six numbers to go in the Daisy from which you can make
all the numbers from 1 to a number bigger than 25?
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?
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!
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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.
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 all the numbers that can be made by adding the dots on two dice.
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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 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
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
If you have ten counters numbered 1 to 10, how many can you put
into pairs that add to 10? Which ones do you have to leave out?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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?
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?