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

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

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?

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

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?

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

Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?

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?

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

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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?

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?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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?

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

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

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

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

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?

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

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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?

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

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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?

Can you fill in the empty boxes in the grid with the right shape and colour?

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

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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

The Zargoes use almost the same alphabet as English. What does this birthday message say?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

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

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

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.

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

Try out the lottery that is played in a far-away land. What is the chance of winning?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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

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

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?