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?
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
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.
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
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?
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.
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?
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?
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
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.
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
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?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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?
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?
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?
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
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?
Four small numbers give the clue to the contents of the four surrounding cells.
In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.
The clues for this Sudoku are the product of the numbers in adjacent squares.
A Sudoku with clues as ratios.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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?
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
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.
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.
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.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
You need to find the values of the stars before you can apply normal Sudoku rules.
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.
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
A Sudoku with clues as ratios.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Label this plum tree graph to make it totally magic!
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Solve the equations to identify the clue numbers in this Sudoku problem.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
The challenge is to find the values of the variables if you are to solve this Sudoku.
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?"