Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
Follow the clues to find the mystery number.
Can you find the chosen number from the grid using the clues?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
What is the best way to shunt these carriages so that each train
can continue its journey?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
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?
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
Can you use the information to find out which cards I have used?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
What could the half time scores have been in these Olympic hockey matches?
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
How many models can you find which obey these rules?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Can you replace the letters with numbers? Is there only one solution in each case?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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?
Number problems at primary level that require careful consideration.
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
Can you find all the different ways of lining up these Cuisenaire
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Investigate the different ways you could split up these rooms so
that you have double the number.
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?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
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. . . .
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Can you substitute numbers for the letters in these sums?