Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
You have been given nine weights, one of which is slightly heavier
than the rest. Can you work out which weight is heavier in just two
weighings of the balance?
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
How many different symmetrical shapes can you make by shading triangles or squares?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Can you replace the letters with numbers? Is there only one
solution in each case?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
This task follows on from Build it Up and takes the ideas into three dimensions!
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
A few extra challenges set by some young NRICH members.
Can you find all the ways to get 15 at the top of this triangle of numbers?
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
Can you use this information to work out Charlie's house number?
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Find out what a "fault-free" rectangle is and try to make some of
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
A package contains a set of resources designed to develop
students’ mathematical thinking. This package places a
particular emphasis on “being systematic” and is
designed to meet. . . .
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
Find out about Magic Squares in this article written for students. Why are they magic?!
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
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?
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This challenge extends the Plants investigation so now four or more children are involved.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.