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Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?

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Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?

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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.

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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?

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This sudoku requires you to have "double vision" - two Sudoku's for the price of one

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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.

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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?

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A Sudoku based on clues that give the differences between adjacent cells.

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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?

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Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

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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.

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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?

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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?

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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.

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Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.

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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.

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The challenge is to find the values of the variables if you are to solve this Sudoku.

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Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

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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?

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Given the products of diagonally opposite cells - can you complete this Sudoku?

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Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

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How many different symmetrical shapes can you make by shading triangles or squares?

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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?

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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?

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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.

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You need to find the values of the stars before you can apply normal Sudoku rules.

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Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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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.

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Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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This Sudoku, based on differences. Using the one clue number can you find the solution?

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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?

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Use the differences to find the solution to this Sudoku.

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You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

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60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

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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.

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An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

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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?

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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.

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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.

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A pair of Sudoku puzzles that together lead to a complete solution.

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Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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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?

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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?