15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
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?
Four small numbers give the clue to the contents of the four surrounding cells.
Use the differences to find the solution to this Sudoku.
A pair of Sudoku puzzles that together lead to a complete solution.
The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
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?
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.
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?
A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
A Sudoku with clues as ratios.
The clues for this Sudoku are the product of the numbers in adjacent squares.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
A few extra challenges set by some young NRICH members.
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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.
A Sudoku with clues as ratios.
It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?
A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!
in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?
This Sudoku requires you to do some working backwards before working forwards.
Use the clues about the shaded areas to help solve 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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
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?
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?"
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
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?
A Sudoku with a twist.
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.
Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
You need to find the values of the stars before you can apply normal Sudoku rules.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.