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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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!
Choose a symbol to put into the number sentence.
Can you hang weights in the right place to make the equaliser
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?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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?
Choose four of the numbers from 1 to 9 to put in the squares so
that the differences between joined squares are odd.
Use the information about Sally and her brother to find out how many children there are in the Brown family.
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Ahmed is making rods using different numbers of cubes. Which rod is
twice the length of his first rod?
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
Find all the numbers that can be made by adding the dots on two dice.
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?
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.
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 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!
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?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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?
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Here is a chance to play a version of the classic Countdown Game.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
You have 5 darts and your target score is 44. How many different
ways could you score 44?
There are nasty versions of this dice game but we'll start with the nice ones...
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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!
Use the number weights to find different ways of balancing the equaliser.
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?
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?
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?
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?
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?