Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

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.

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 work out how to balance this equaliser? You can put more than one weight on a hook.

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?

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

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

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

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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

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

This task follows on from Build it Up and takes the ideas into three dimensions!

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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

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

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

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?

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

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

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....?

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?

How many possible necklaces can you find? And how do you know you've found them all?

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

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?

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

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.

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

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

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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

Can you use this information to work out Charlie's house number?

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?

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?

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.

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

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

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

This challenge is about finding the difference between numbers which have the same tens digit.

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?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

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

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

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

This article for primary teachers suggests ways in which to help children become better at working systematically.

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?