Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
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?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
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?
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.
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 task encourages you to investigate the number of edging pieces and panes in different sized windows.
This Sudoku requires you to do some working backwards before working forwards.
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.
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
By selecting digits for an addition grid, what targets can you make?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
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?
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
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.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
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.
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?
A Sudoku with a twist.
Can you replace the letters with numbers? Is there only one solution in each case?
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?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
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?
You need to find the values of the stars before you can apply normal Sudoku rules.
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.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Given the products of diagonally opposite cells - can you complete this Sudoku?
A Sudoku with clues as ratios or fractions.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?
Given the products of adjacent cells, can you complete this Sudoku?
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...
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly Â£100 if the prices are Â£10 for adults, 50p for pensioners and 10p for children.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.