How many solutions can you find to this sum? Each of the different letters stands for a different number.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five 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?
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?
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.
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 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. . . .
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous 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.
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?
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.
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
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?"
A few extra challenges set by some young NRICH members.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative 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?
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 man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
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 challenging activity focusing on finding all possible ways of stacking rods.
This challenge extends the Plants investigation so now four or more children are involved.
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?
How many different symmetrical shapes can you make by shading triangles or squares?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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.
Can you find all the different triangles on these peg boards, and
find their angles?
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
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?
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
Can you substitute numbers for the letters in these sums?
In this matching game, you have to decide how long different events take.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?