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?
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
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?
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.
Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?
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.
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
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.
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?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?
Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
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.
Four small numbers give the clue to the contents of the four surrounding cells.
Find out about Magic Squares in this article written for students. Why are they magic?!
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
A pair of Sudoku puzzles that together lead to a complete solution.
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.
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
This Sudoku requires you to do some working backwards before working forwards.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
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...
A Sudoku with clues as ratios.
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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.
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?
The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .
A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
A Sudoku with a twist.
You need to find the values of the stars before you can apply normal Sudoku rules.
Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.
Use the differences to find the solution to this Sudoku.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
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!
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?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
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.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?