Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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

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?

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

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

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?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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

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

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

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?

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

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

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

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using 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?

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

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

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

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

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?

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?

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?

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

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

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.?

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?

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

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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.

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?

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

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.

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?

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?

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?

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?

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?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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?

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

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.