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?

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

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?

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!

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?

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

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

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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

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?

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?

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?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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

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?

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

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

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?

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

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?

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

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.

These activities lend themselves to systematic working in the sense that it helps if you 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?

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

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.

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

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.

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

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

Can you substitute numbers for the letters in these sums?

There are lots of different methods to find out what the shapes are worth - how many can you find?

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?

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?

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?

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