Can you work out how to win this game of Nim? Does it matter if you go first or second?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Nim-7 game for an adult and child. Who will be the one to take the last counter?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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.
How many moves does it take to swap over some red and blue frogs? Do you have a method?
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?
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.
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
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.
A package contains a set of resources designed to develop
pupils’ mathematical thinking. This package places a
particular emphasis on “generalising” and is designed
to meet the. . . .
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.
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?
This challenge asks you to imagine a snake coiling on itself.
Stop the Clock game for an adult and child. How can you make sure you always win this game?
A collection of games on the NIM theme
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.
Find out what a "fault-free" rectangle is and try to make some of
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
This challenge is about finding the difference between numbers which have the same tens digit.
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?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
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?
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?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Find the sum of all three-digit numbers each of whose digits is
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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.
Got It game for an adult and child. How can you play so that you know you will always win?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
This activity involves rounding four-digit numbers to the nearest thousand.
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.
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?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
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
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?