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How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

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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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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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If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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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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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. . . .

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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?

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Two sudokus in one. Challenge yourself to make the necessary connections.

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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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. . . .

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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?

Find out about Magic Squares in this article written for students. Why are they magic?!

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Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

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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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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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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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Four small numbers give the clue to the contents of the four surrounding cells.

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Use the differences to find the solution to this 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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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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This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

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A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly Â£100 if the prices are Â£10 for adults, 50p for pensioners and 10p for children.

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

A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.

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Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!

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

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

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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 cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

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I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

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Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

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Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

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By selecting digits for an addition grid, what targets can you make?

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In this game you are challenged to gain more columns of lily pads than your opponent.

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Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

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A challenging activity focusing on finding all possible ways of stacking rods.

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This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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This challenge extends the Plants investigation so now four or more children are involved.

An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.

In this article, the NRICH team describe the process of selecting solutions for publication on the site.

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

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Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?