This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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. . . .
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.
A few extra challenges set by some young NRICH members.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
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.
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.
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.
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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 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?"
In this matching game, you have to decide how long different events take.
This challenge extends the Plants investigation so now four or more children are involved.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
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. . . .
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?
Given the products of adjacent cells, can you complete this Sudoku?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
The Vikings communicated in writing by making simple scratches on
wood or stones called runes. Can you work out how their code works
using the table of the alphabet?
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
I like to walk along the cracks of the paving stones, but not the
outside edge of the path itself. How many different routes can you
find for me to take?
Ana and Ross looked in a trunk in the attic. They found old cloaks
and gowns, hats and masks. How many possible costumes could they
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.