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.
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
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 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?
A Sudoku with clues as ratios or fractions.
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.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Given the products of diagonally opposite cells - can you complete this Sudoku?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
A Sudoku with a twist.
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 Sudoku with clues as ratios.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
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?
A Sudoku with a twist.
You need to find the values of the stars before you can apply normal Sudoku rules.
Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
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?
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 clues as ratios.
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
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?
By selecting digits for an addition grid, what targets can you make?
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?
Solve the equations to identify the clue numbers in this Sudoku 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.
This Sudoku requires you to do some working backwards before working forwards.
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 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.
A Sudoku that uses transformations as supporting clues.
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
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.
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.
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
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?
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!
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
How many different differences can you make?
How many different symmetrical shapes can you make by shading triangles or squares?
This Sudoku combines all four arithmetic operations.
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 monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?
Use the clues about the shaded areas to help solve this sudoku