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.
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?
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
By selecting digits for an addition grid, what targets can you make?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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.
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?
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?
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
This Sudoku requires you to do some working backwards before working forwards.
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
A Sudoku with a twist.
How many different differences can you make?
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?
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?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
A Sudoku with clues as ratios.
A Sudoku with a twist.
You need to find the values of the stars before you can apply normal Sudoku rules.
A Sudoku with clues as ratios or fractions.
Given the products of diagonally opposite cells - can you complete this Sudoku?
A Sudoku with clues as ratios.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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?
This Sudoku, based on differences. Using the one clue number can you find the solution?
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?
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.
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
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.
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?
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.
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 arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
Given the products of adjacent cells, can you complete this Sudoku?
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
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...
How many different symmetrical shapes can you make by shading triangles or squares?
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 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.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Use the differences to find the solution to this Sudoku.
Find out about Magic Squares in this article written for students. Why are they magic?!
Use the clues about the shaded areas to help solve this sudoku