What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

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?

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

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

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?

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

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

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

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

How will you go about finding all the jigsaw pieces that have one peg and one hole?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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

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

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?

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

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?

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?

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?

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.

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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

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

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?

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?

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

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

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

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?

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

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?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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

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?

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

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

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

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

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

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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

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