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

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

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

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

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?

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

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.

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

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?

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

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

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

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

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

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.

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.

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 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?

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

A game for 2 players with similaritlies to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.

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.

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?

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

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

What happens when you round these three-digit numbers to the nearest 100?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

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

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

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

What happens when you round these numbers to the nearest whole number?

It starts quite simple but great opportunities for number discoveries and patterns!

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

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?

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

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

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?

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

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

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

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?

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.

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?

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

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.