Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
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 it up?
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?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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 in them?
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?
Find your way through the grid starting at 2 and following these operations. What number do you end on?
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
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 cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these two grids?
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 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?
Use the clues to colour each square.
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.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
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 jugs.
Can you find all the different ways of lining up these Cuisenaire rods?
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?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
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?
Investigate the different ways you could split up these rooms so that you have double the number.
How many different triangles can you make on a circular pegboard that has nine pegs?
A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?
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?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
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.
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!
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?
This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?
Find all the numbers that can be made by adding the dots on two dice.
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?
If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?
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?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
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.
Can you fill in the empty boxes in the grid with the right shape and colour?
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?
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?