Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?
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?
A collection of games on the NIM theme
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
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.
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.
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Are these statements always true, sometimes true or never true?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
It starts quite simple but great opportunities for number discoveries and patterns!
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
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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.
Here are two kinds of spirals for you to explore. What do you notice?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
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.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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?
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.
This activity involves rounding four-digit numbers to the nearest thousand.
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?
This challenge asks you to imagine a snake coiling on itself.
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?
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
This activity focuses on rounding to the nearest 10.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
This challenge is about finding the difference between numbers which have the same tens digit.
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Stop the Clock game for an adult and child. How can you make sure you always win this game?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
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?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Got It game for an adult and child. How can you play so that you know you will always win?
How many centimetres of rope will I need to make another mat just
like the one I have here?
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?
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?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
How many moves does it take to swap over some red and blue frogs? Do you have a method?
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
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?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?