Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?"
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.
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. . . .
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
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?
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Given the products of adjacent cells, can you complete this Sudoku?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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.
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.
Special clue numbers related to the difference between numbers in
two adjacent cells and values of the stars in the "constellation"
make this a doubly interesting problem.
The clues for this Sudoku are the product of the numbers in adjacent squares.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
This Sudoku, based on differences. Using the one clue number can you find the solution?
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.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
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?
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
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...
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
A few extra challenges set by some young NRICH members.
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?
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.
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?
This challenge extends the Plants investigation so now four or more children are involved.
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.
Find out about Magic Squares in this article written for students. Why are they magic?!
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 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 tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
Use the differences to find the solution to this Sudoku.
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?
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?
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.