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.
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Find out what a "fault-free" rectangle is and try to make some of
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
Can you work out how to win this game of Nim? Does it matter if you go first or second?
Stop the Clock game for an adult and child. How can you make sure you always win this game?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
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.
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
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?
Can you find all the ways to get 15 at the top of this triangle of numbers?
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?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
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 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.
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 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.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
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?
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?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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.
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?
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?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
This activity involves rounding four-digit numbers to the nearest thousand.
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?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
This activity focuses on rounding to the nearest 10.
Find the sum of all three-digit numbers each of whose digits is
What happens when you round these three-digit numbers to the nearest 100?
What happens when you round these numbers to the nearest whole number?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in