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?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
The challenge is to find the values of the variables if you are to solve this Sudoku.
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?
A Sudoku with a twist.
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
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.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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.
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.
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 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.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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?
Label this plum tree graph to make it totally magic!
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.
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?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?
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...
You need to find the values of the stars before you can apply normal Sudoku rules.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
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.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
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.
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?
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?
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?
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
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?"
Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
Given the products of adjacent cells, can you complete this Sudoku?
Use the clues about the shaded areas to help solve this sudoku
A Sudoku based on clues that give the differences between adjacent cells.
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.
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
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?
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 pair of Sudoku puzzles that together lead to a complete solution.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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.