Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
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?
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?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
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?
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
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.
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Two sudokus in one. Challenge yourself to make the necessary
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?
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?
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
A Sudoku with clues given as sums of entries.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
Solve this Sudoku puzzle whose clues are in the form of sums of the
numbers which should appear in diagonal opposite cells.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
A Sudoku that uses transformations as supporting clues.
A Sudoku with clues as ratios.
A Sudoku with a twist.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
How many models can you find which obey these rules?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
This activity investigates how you might make squares and pentominoes from Polydron.
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.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Given the products of diagonally opposite cells - can you complete this Sudoku?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
How many triangles can you make on the 3 by 3 pegboard?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
A Sudoku with clues as ratios or fractions.