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.
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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 work out how to win this game of Nim? Does it matter if you go first or second?
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.
Find out what a "fault-free" rectangle is and try to make some of
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
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 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?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
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!
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.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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 the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
This challenge asks you to imagine a snake coiling on itself.
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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 challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
Here are two kinds of spirals for you to explore. 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.
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
A collection of games on the NIM theme
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
Start with any number of counters in any number of piles. 2 players
take it in turns to remove any number of counters from a single
pile. The winner is the player to take the last counter.