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?

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

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

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

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

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?

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

Find all the numbers that can be made by adding the dots on two dice.

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?

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?

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?

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?

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

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

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

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?

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

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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?

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?

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?

How many different rectangles can you make using this set of rods?

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

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

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

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

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?

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?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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?

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

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

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

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

You have 5 darts and your target score is 44. How many different ways could you score 44?

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?

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 Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

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

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

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....?

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?

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.

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

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?

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

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

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

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 working in a systematic way will ensure none are left out.