What is the best way to shunt these carriages so that each train can continue its journey?

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?

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?

Try this matching game which will help you recognise different ways of saying the same time interval.

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?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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?

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?

What happens when you try and fit the triomino pieces into these two grids?

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

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 work out how to balance this equaliser? You can put more than one weight on a hook.

How many trains can you make which are the same length as Matt's, using rods that are identical?

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 find all the different ways of lining up these Cuisenaire rods?

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

Find out what a "fault-free" rectangle is and try to make some of your own.

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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?

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Can you find out in which order the children are standing in this line?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

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 information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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?

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?

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

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?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

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?

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Find your way through the grid starting at 2 and following these operations. What number do you end on?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

How many different triangles can you make on a circular pegboard that has nine pegs?

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?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?