Nim-7 game for an adult and child. Who will be the one to take the last counter?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Got It game for an adult and child. How can you play so that you know you will always win?
Find out what a "fault-free" rectangle is and try to make some of
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
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
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
How could Penny, Tom and Matthew work out how many chocolates there
are in different sized boxes?
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?
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
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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.
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?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
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.
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?
An investigation that gives you the opportunity to make and justify
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Here are two kinds of spirals for you to explore. What do you notice?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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
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?
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 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.
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
Are these statements always true, sometimes true or never true?
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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?
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
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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.