Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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?
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?
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?
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
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.
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.
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.
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.
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
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.
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 pair of Sudoku puzzles that together lead to a complete solution.
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?
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
Four small numbers give the clue to the contents of the four surrounding cells.
A Sudoku with a twist.
A Sudoku with clues as ratios.
This Sudoku, based on differences. Using the one clue number can you find the solution?
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.
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.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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?
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?
A Sudoku with a twist.
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?
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?
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
Solve the equations to identify the clue numbers in this Sudoku problem.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
This Sudoku requires you to do some working backwards before working forwards.
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?
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!
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
Use the differences to find the solution to this Sudoku.
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?
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?
Find out about Magic Squares in this article written for students. Why are they magic?!
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. . . .
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?
Two sudokus in one. Challenge yourself to make the necessary connections.