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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?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .
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?"
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?
A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?
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...
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?
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 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.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Given the products of adjacent cells, can you complete this Sudoku?
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 letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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.
A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Given the products of diagonally opposite cells - can you complete this Sudoku?
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
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.
A few extra challenges set by some young NRICH members.
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?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
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.
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
This Sudoku, based on differences. Using the one clue number can you find the solution?
A Sudoku that uses transformations as supporting clues.
Two sudokus in one. Challenge yourself to make the necessary connections.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
Can you coach your rowing eight to win?
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
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.
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?
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.
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
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?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
A Sudoku based on clues that give the differences between adjacent cells.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?