If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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.
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
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 solutions can you find to this sum? Each of the different letters stands for a different number.
A Sudoku with a twist.
You need to find the values of the stars before you can apply normal Sudoku rules.
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.
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.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.
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?
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.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
A Sudoku with clues as ratios or fractions.
A Sudoku with a twist.
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?
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.
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"?
A Sudoku based on clues that give the differences between adjacent cells.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Label this plum tree graph to make it totally magic!
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?
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
By selecting digits for an addition grid, what targets can you make?
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?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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?
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?
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!
Solve the equations to identify the clue numbers in this Sudoku problem.
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
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?
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.
Use the clues about the shaded areas to help solve this sudoku
Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?
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. . . .
Two sudokus in one. Challenge yourself to make the necessary connections.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
A Sudoku with clues as ratios.
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?
A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.