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?
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?
Solve the equations to identify the clue numbers in this Sudoku problem.
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.
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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.
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.
The challenge is to find the values of the variables if you are to solve this Sudoku.
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?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
The clues for this Sudoku are the product of the numbers in adjacent squares.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
A Sudoku with a twist.
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
A Sudoku with a twist.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
How many different symmetrical shapes can you make by shading triangles or squares?
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
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?
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...
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.
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?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Use the differences to find the solution to this Sudoku.
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
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?
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?
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?
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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.
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?
Label this plum tree graph to make it totally magic!
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
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?
A Sudoku with clues as ratios.
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?
A pair of Sudoku puzzles that together lead to a complete solution.
You need to find the values of the stars before you can apply normal Sudoku rules.
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.
Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?