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?
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.
The challenge is to find the values of the variables if you are to solve this Sudoku.
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
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?
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?
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?
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
A Sudoku with a twist.
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.
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?
A Sudoku with a twist.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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.
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
Label this plum tree graph to make it totally magic!
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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?
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?
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?
Solve the equations to identify the clue numbers in this Sudoku problem.
Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?
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.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Find out about Magic Squares in this article written for students. Why are they magic?!
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
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 have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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?
Use the differences to find the solution to this Sudoku.
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...
You need to find the values of the stars before you can apply normal Sudoku rules.
Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?
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?
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
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.
A Sudoku that uses transformations as supporting clues.
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Use the clues about the shaded areas to help solve 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?
How many different symmetrical shapes can you make by shading triangles or squares?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.
A challenging activity focusing on finding all possible ways of stacking rods.