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 letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
A few extra challenges set by some young NRICH members.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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 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.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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.
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?"
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?
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?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
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.
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?
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.
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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 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 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?
Can you use the information to find out which cards I have used?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
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. . . .
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
Given the products of adjacent cells, can you complete this Sudoku?
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?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
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?
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?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?