What is the least number of moves you can take to rearrange the
bears so that no bear is next to a bear of the same colour?
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?
Use the clues to colour each square.
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?
Jack has nine tiles. He put them together to make a square so that
two tiles of the same colour were not beside each other. Can you
find another way to do it?
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
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three
square grid, so that there is only one of each colour in every row
and every column
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
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 eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue.
She wants to fit them together to make a cube so that each colour shows on each face just once.
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way
to share the sweets between the three children so they each get the
kind they like. Is there more than one way to do it?
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
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 8 in the circles so that no consecutive
numbers are joined by a line.
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
How many trains can you make which are the same length as Matt's,
using rods that are identical?
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 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?
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
Investigate the different ways you could split up these rooms so
that you have double the number.
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.
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?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
Can you fill in the empty boxes in the grid with the right shape
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Find all the numbers that can be made by adding the dots on two dice.
This 100 square jigsaw is written in code. It starts with 1 and
ends with 100. Can you build it up?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Imagine that the puzzle pieces of a jigsaw are roughly a
rectangular shape and all the same size. How many different puzzle
pieces could there be?
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
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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 find all the different ways of lining up these Cuisenaire
How many different triangles can you make on a circular pegboard
that has nine pegs?
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!
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 put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?