Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
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.
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?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Given the products of adjacent cells, can you complete this Sudoku?
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.
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?"
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.
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?
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
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 diagonally opposite cells - can you complete 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.
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.
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?
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.
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?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
Use the differences to find the solution to this Sudoku.
Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting problem.
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?
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?
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.
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
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?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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?
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?
Use the clues about the shaded areas to help solve this sudoku
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?
A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?
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?
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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.
A Sudoku with a twist.
Four small numbers give the clue to the contents of the four surrounding cells.
Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?
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?
A challenging activity focusing on finding all possible ways of stacking rods.
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.
Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
A Sudoku with clues as ratios.