Label this plum tree graph to make it totally magic!
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.
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?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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?
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.
Solve the equations to identify the clue numbers in this Sudoku problem.
The challenge is to find the values of the variables if you are 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 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.
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
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.
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?
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?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
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?
A Sudoku with a twist.
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?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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?
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
A pair of Sudoku puzzles that together lead to a complete solution.
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 Sudoku, based on differences. Using the one clue number can you find the solution?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Two sudokus in one. Challenge yourself to make the necessary connections.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Given the products of diagonally opposite cells - can you complete 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. . . .
A Sudoku that uses transformations as supporting clues.
A Sudoku with clues as ratios.
This Sudoku combines all four arithmetic operations.
Find out about Magic Squares in this article written for students. Why are they magic?!
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.
A Sudoku with clues as ratios.
A Sudoku with clues given as sums of entries.
Four small numbers give the clue to the contents of the four surrounding cells.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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 second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
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.
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?
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
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?