Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
Given the products of adjacent cells, can you complete this 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?
A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
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.
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?
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
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?"
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...
The clues for this Sudoku are the product of the numbers in adjacent squares.
A pair of Sudoku puzzles that together lead to a complete solution.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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 with clues as ratios or fractions.
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
Given the products of diagonally opposite cells - can you complete this Sudoku?
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 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 a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
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?
Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?
Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
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?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
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!
Use the clues about the shaded areas to help solve this sudoku
You need to find the values of the stars before you can apply normal Sudoku rules.
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
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?
Two sudokus in one. Challenge yourself to make the necessary connections.
Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?
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.
A Sudoku with clues as ratios.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
This Sudoku, based on differences. Using the one clue number can you find the solution?
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. . . .
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.