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?
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?
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.
Four small numbers give the clue to the contents of the four
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?
A Sudoku with clues as ratios.
A Sudoku with a twist.
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. . . .
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
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.
A Sudoku based on clues that give the differences between adjacent cells.
You need to find the values of the stars before you can apply normal Sudoku rules.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
This Sudoku, based on differences. Using the one clue number can you find the solution?
Two sudokus in one. Challenge yourself to make the necessary
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.
Use the differences to find the solution to this Sudoku.
Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
A Sudoku that uses transformations as supporting clues.
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.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
A pair of Sudoku puzzles that together lead to a complete solution.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
A Sudoku with clues as ratios or fractions.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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.
Label this plum tree graph to make it totally magic!
A Sudoku with clues given as sums of entries.
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.
Solve the equations to identify the clue numbers in this Sudoku problem.
Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's
there is one digit, between the two 2's there are two digits, and
between the two 3's there are three digits.
Imagine a stack of numbered cards with one on top. Discard the top,
put the next card to the bottom and repeat continuously. Can you
predict the last card?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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?
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?
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
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?
This sudoku requires you to have "double vision" - two Sudoku's for
the price of one
Use the clues about the shaded areas to help solve this sudoku
This Sudoku requires you to do some working backwards before working forwards.
In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.
This Sudoku combines all four arithmetic operations.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.