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.
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?"
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.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Given the products of adjacent cells, can you complete this Sudoku?
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?
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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...
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
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.
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 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?
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?
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.
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.
Four small numbers give the clue to the contents of the four surrounding cells.
Use the differences to find the solution to this Sudoku.
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 Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.
Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
This Sudoku, based on differences. Using the one clue number can you find the solution?
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 nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
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?
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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
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?
This challenge extends the Plants investigation so now four or more children are involved.
A Sudoku with a twist.
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?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
A Sudoku with clues as ratios.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
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?
Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?