Can you recreate these designs? What are the basic units? What
movement is required between each unit? Some elegant use of
procedures will help - variables not essential.
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
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?
Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?
Four small numbers give the clue to the contents of the four
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. . . .
A Sudoku based on clues that give the differences between adjacent cells.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find 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.
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.
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?
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
A Sudoku with clues as ratios.
A Sudoku that uses transformations as supporting clues.
You need to find the values of the stars before you can apply normal Sudoku rules.
Two sudokus in one. Challenge yourself to make the necessary
A pair of Sudoku puzzles that together lead to a complete solution.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
A Sudoku with clues given as sums of entries.
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
Use the clues about the shaded areas to help solve this sudoku
This sudoku requires you to have "double vision" - two Sudoku's for
the price of one
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?
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
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?
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 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.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Solve the equations to identify the clue numbers in this Sudoku problem.
This Sudoku combines all four arithmetic operations.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
A Sudoku with clues as ratios or fractions.
This Sudoku, based on differences. Using the one clue number can you find the solution?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
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 diagonally opposite cells - can you complete this Sudoku?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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.
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.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
An introduction to bond angle geometry.
A Sudoku with a twist.
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?