I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
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?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
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.
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.
The challenge is to find the values of the variables if you are to solve this Sudoku.
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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?
You need to find the values of the stars before you can apply normal Sudoku rules.
A Sudoku with a twist.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
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?
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.
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 NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
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?
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
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.
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.
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.
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 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?
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
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?
Solve the equations to identify the clue numbers in this Sudoku problem.
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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?
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.
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?
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
A pair of Sudoku puzzles that together lead to a complete solution.
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?
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?
This Sudoku combines all four arithmetic operations.
A Sudoku with clues as ratios.
Four small numbers give the clue to the contents of the four surrounding cells.
How many different symmetrical shapes can you make by shading triangles or squares?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
Use the clues about the shaded areas to help solve this sudoku
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. . . .
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?