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?

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

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

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

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

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?

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

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

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!

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

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

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?

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.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

What happens when you round these three-digit numbers to the nearest 100?

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

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

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

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!

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?

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?

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

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

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?

Can you substitute numbers for the letters in these sums?

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

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.

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 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?

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

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

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

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

What happens when you round these numbers to the nearest whole number?

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?

What is the smallest number of coins needed to make up 12 dollars and 83 cents?

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.

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?

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.?

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

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.

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

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?

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

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

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?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

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?