An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
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?
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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 find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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.
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Use the differences to find the solution to this Sudoku.
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.
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...
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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?
How many different symmetrical shapes can you make by shading triangles or squares?
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.
Find out about Magic Squares in this article written for students. Why are they magic?!
Label this plum tree graph to make it totally magic!
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
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.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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.
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
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 particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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.
A few extra challenges set by some young NRICH members.
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
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?"
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 values of the nine letters in the sum: FOOT + BALL = GAME
The challenge is to find the values of the variables if you are to
solve this Sudoku.
Four small numbers give the clue to the contents of the four
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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?
A pair of Sudoku puzzles that together lead to a complete solution.