Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
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.
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
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?
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
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 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?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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?
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.
Given the products of adjacent cells, can you complete this Sudoku?
A few extra challenges set by some young NRICH members.
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
This package contains a collection of problems from the NRICH
website that could be suitable for students who have a good
understanding of Factors and Multiples and who feel ready to take
on some. . . .
This challenge extends the Plants investigation so now four or more children are involved.
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?
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?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
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?
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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.
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. . . .
A challenging activity focusing on finding all possible ways of stacking rods.
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
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.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
How many different symmetrical shapes can you make by shading triangles or squares?
Find out about Magic Squares in this article written for students. Why are they magic?!
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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?