Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Have a go at balancing this equation. Can you find different ways of doing it?

Can you find the chosen number from the grid using the clues?

Can you work out some different ways to balance this equation?

Can you replace the letters with numbers? Is there only one solution in each case?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

What two-digit numbers can you make with these two dice? What can't you make?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

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

Investigate the different ways you could split up these rooms so that you have double the number.

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

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

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.

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 many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

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?

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.

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.

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?

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?

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?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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

On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?

In how many ways can you stack these rods, following the rules?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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?

What could the half time scores have been in these Olympic hockey matches?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

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!

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

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

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

Can you make square numbers by adding two prime numbers together?