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?
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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?
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
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?
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.
This Sudoku, based on differences. Using the one clue number can you find the solution?
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.
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.
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
A pair of Sudoku puzzles that together lead to a complete solution.
How many different symmetrical shapes can you make by shading triangles or squares?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Use the differences to find the solution to this Sudoku.
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?
Four small numbers give the clue to the contents of the four
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?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Label this plum tree graph to make it totally magic!
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
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?
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.
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
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.
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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...
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?
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.
Given the products of adjacent cells, can you complete this Sudoku?
Rather than using the numbers 1-9, this sudoku uses the nine
different letters used to make the words "Advent Calendar".
You need to find the values of the stars before you can apply normal Sudoku rules.
This sudoku requires you to have "double vision" - two Sudoku's for
the price of one
A Sudoku with clues given as sums of entries.
A Sudoku with clues as ratios.
Two sudokus in one. Challenge yourself to make the necessary
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. . . .
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.
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?