Can you work out how to win this game of Nim? Does it matter if you go first or second?
Nim-7 game for an adult and child. Who will be the one to take 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
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.
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
How many moves does it take to swap over some red and blue frogs? Do you have a method?
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.
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.
It starts quite simple but great opportunities for number discoveries and patterns!
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Are these statements relating to odd and even numbers always true, sometimes true or never true?
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 asks you to imagine a snake coiling on itself.
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
Here are two kinds of spirals for you to explore. What do you notice?
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?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
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?
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
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
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.
A collection of games on the NIM theme
Stop the Clock game for an adult and child. How can you make sure you always win this game?
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
This activity involves rounding four-digit numbers to the nearest thousand.
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Can you find all the ways to get 15 at the top of this triangle of numbers?
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?
Got It game for an adult and child. How can you play so that you know you will always win?
This task follows on from Build it Up and takes the ideas into three dimensions!
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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.
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?
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.
This activity focuses on rounding to the nearest 10.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This challenge is about finding the difference between numbers which have the same tens digit.
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.