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?
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.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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 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
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.
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?
It starts quite simple but great opportunities for number discoveries and patterns!
Here are two kinds of spirals for you to explore. What do you notice?
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. . . .
This challenge asks you to imagine a snake coiling on itself.
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?
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?
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?
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
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?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Find out what a "fault-free" rectangle is and try to make some of
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
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
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
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.
Stop the Clock game for an adult and child. How can you make sure you always win this game?
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 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.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
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?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
This task follows on from Build it Up and takes the ideas into three dimensions!
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
While we were sorting some papers we found 3 strange sheets which
seemed to come from small books but there were page numbers at the
foot of each page. Did the pages come from the same book?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.