Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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

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

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.

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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

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

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?

This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.

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?

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

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

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.

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?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

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

Find out what a "fault-free" rectangle is and try to make some of your own.

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

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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?

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?

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

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

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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.

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

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

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?

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

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

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

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

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?

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?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Try this matching game which will help you recognise different ways of saying the same time interval.

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

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?