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

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

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?

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?

An investigation that gives you the opportunity to make and justify predictions.

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

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

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

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

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?

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?

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?

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

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

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

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

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?

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?

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

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

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

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

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

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.

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

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?

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

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?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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 find the chosen number from the grid using the clues?

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

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

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

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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

Find out about Magic Squares in this article written for students. Why are they magic?!

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?

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?

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

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

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?