The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?

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

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

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

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

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

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

Can you find out in which order the children are standing in this line?

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

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?

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

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

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

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?

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

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

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

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?

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.

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

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?

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

These practical challenges are all about making a 'tray' and covering it with paper.

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

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

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?

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 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.

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?

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

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

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?

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

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.

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.

What happens when you try and fit the triomino pieces into these two grids?

Find your way through the grid starting at 2 and following these operations. What number do you end on?

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

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?

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

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?

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.

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?

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?

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?