Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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?
This challenge extends the Plants investigation so now four or more children are involved.
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
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.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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 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?
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?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
Can you use the information to find out which cards I have used?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Use the differences to find the solution to this Sudoku.
Four small numbers give the clue to the contents of the four
Four friends must cross a bridge. How can they all cross it in just
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
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?
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
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?
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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.
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?
Can you substitute numbers for the letters in these sums?
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
A few extra challenges set by some young NRICH members.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Follow the clues to find the mystery number.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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....?
Find out about Magic Squares in this article written for students. Why are they magic?!
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
An investigation that gives you the opportunity to make and justify