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?
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.
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?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
The clues for this Sudoku are the product of the numbers in adjacent squares.
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"?
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 student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"
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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
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.
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 task encourages you to investigate the number of edging pieces and panes in different sized windows.
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?
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 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.
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.
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 clues as ratios.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
A Sudoku with a twist.
Four small numbers give the clue to the contents of the four surrounding cells.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
Given the products of adjacent cells, can you complete this Sudoku?
You need to find the values of the stars before you can apply normal Sudoku rules.
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 pair of Sudoku puzzles that together lead to a complete solution.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Find out about Magic Squares in this article written for students. Why are they magic?!
A Sudoku with clues as ratios.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
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!
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
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 requires you to do some working backwards before working forwards.
A Sudoku with a twist.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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?
Solve the equations to identify the clue numbers in this Sudoku problem.
Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
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...
Two sudokus in one. Challenge yourself to make the necessary connections.
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?