Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
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?
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
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.
Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
This Sudoku combines all four arithmetic operations.
A Sudoku based on clues that give the differences between adjacent cells.
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 clue number in this sudoku is the product of the two numbers in adjacent cells.
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?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
Two sudokus in one. Challenge yourself to make the necessary
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, based on differences. Using the one clue number can you find the solution?
A Sudoku that uses transformations as supporting clues.
The letters of the word ABACUS have been arranged in the shape of a
triangle. How many different ways can you find to read the word
ABACUS from this triangular pattern?
It is possible to identify a particular card out of a pack of 15
with the use of some mathematical reasoning. What is this reasoning
and can it be applied to other numbers of cards?
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
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.
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.
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.
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 clues about the shaded areas to help solve this sudoku
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.
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.
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?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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?
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
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
This Sudoku requires you to do some working backwards before working forwards.
Solve the equations to identify the clue numbers in this Sudoku problem.
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
A Sudoku with clues as ratios.
An introduction to bond angle geometry.
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.
Four small numbers give the clue to the contents of the four
This package contains a collection of problems from the NRICH
website that could be suitable for students who have a good
understanding of Factors and Multiples and who feel ready to take
on some. . . .
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?