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?
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?
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?
Find out about Magic Squares in this article written for students. Why are they magic?!
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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.
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?
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.
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.
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.
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.
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?
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 arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
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.
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?
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
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?
A Sudoku with a twist.
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
You need to find the values of the stars before you can apply normal Sudoku rules.
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?
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...
Given the products of adjacent cells, can you complete this Sudoku?
Four small numbers give the clue to the contents of the four surrounding cells.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Given the products of diagonally opposite cells - can you complete this Sudoku?
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.
A Sudoku with clues as ratios.
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.
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?
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.
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?
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
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 Sudoku with clues as ratios.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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?
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?