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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
You need to find the values of the stars before you can apply normal Sudoku rules.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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 in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
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.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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 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?
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.
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.
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.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
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.
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
A Sudoku with a twist.
Find out about Magic Squares in this article written for students. Why are they magic?!
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Given the products of adjacent cells, can you complete this Sudoku?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
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.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
This Sudoku, based on differences. Using the one clue number can you find the solution?
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
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
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?
Solve the equations to identify the clue numbers in this Sudoku problem.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Label this plum tree graph to make it totally magic!
The challenge is to find the values of the variables if you are to
solve 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?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
This Sudoku combines all four arithmetic operations.
A man has 5 coins in his pocket. Given the clues, can you work out
what the coins are?
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 particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
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.
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?