Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?
Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?
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 second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
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
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.
Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?
A Sudoku based on clues that give the differences between adjacent cells.
in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
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.
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?
Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?
Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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.
The challenge is to find the values of the variables if you are to solve this Sudoku.
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
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?
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?
How many different symmetrical shapes can you make by shading triangles or squares?
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?
A Sudoku with clues as ratios.
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?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
You need to find the values of the stars before you can apply normal Sudoku rules.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Four small numbers give the clue to the contents of the four surrounding cells.
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.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
This Sudoku, based on differences. Using the one clue number can you find the solution?
A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?
A Sudoku with clues as ratios.
A Sudoku with a twist.
Use the differences to find the solution to this Sudoku.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
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?
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.
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.
A pair of Sudoku puzzles that together lead to a complete solution.
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
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?
Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?