The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

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

The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

My coat has three buttons. How many ways can you find to do up all the buttons?

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?

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

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

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

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?

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?

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?

How many different shapes can you make by putting four right- angled isosceles triangles together?

This challenge is about finding the difference between numbers which have the same tens digit.

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

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?

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

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

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

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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

Using the statements, can you work out how many of each type of rabbit there are in these pens?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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?

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

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

These practical challenges are all about making a 'tray' and covering it with paper.

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?

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?

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?

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 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 jugs.

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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

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 find all the ways to get 15 at the top of this triangle of numbers?

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

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?

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?

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!

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.