This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

Nim-7 game for an adult and child. Who will be the one to take the last counter?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

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 game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

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

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

Got It game for an adult and child. How can you play so that you know you will always win?

Are these statements relating to odd and even numbers always true, sometimes true or never true?

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

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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

Here are two kinds of spirals for you to explore. What do you notice?

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

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

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

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.

Stop the Clock game for an adult and child. How can you make sure you always win this game?

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

Can you find all the ways to get 15 at the top of this triangle of numbers?

Are these statements always true, sometimes true or never true?

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?

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

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

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?

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

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

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

Can you work out how to win this game of Nim? Does it matter if you go first or second?

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

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.

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

This activity involves rounding four-digit numbers to the nearest thousand.