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.
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?
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.
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.
The challenge is to find the values of the variables if you are to
solve this Sudoku.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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?
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
A Sudoku with a twist.
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
You need to find the values of the stars before you can apply normal Sudoku rules.
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?
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?
How many different symmetrical shapes can you make by shading triangles or squares?
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?
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?
Find out about Magic Squares in this article written for students. Why are they magic?!
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Solve the equations to identify the clue numbers in this Sudoku problem.
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?
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
Label this plum tree graph to make it totally magic!
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.
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?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the 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?
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
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?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
If you are given the mean, median and mode of five positive whole
numbers, can you find the numbers?
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.
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...
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
A pair of Sudoku puzzles that together lead to a complete solution.
This Sudoku combines all four arithmetic operations.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
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 have only 40 metres of fencing available, what is the maximum area of land you can fence off?
The puzzle can be solved with the help of small clue-numbers which
are either placed on the border lines between selected pairs of
neighbouring squares of the grid or placed after slash marks on. . . .
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
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?
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?
Two sudokus in one. Challenge yourself to make the necessary
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.