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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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A, B & C own a half, a third and a sixth of a coin collection. Each grab some coins, return some, then share equally what they had put back, finishing with their own share. How rich are they?

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There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

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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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What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?

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Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

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Show that all pentagonal numbers are one third of a triangular number.

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15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?

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Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?

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First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...

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The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

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Make some loops out of regular hexagons. What rules can you discover?

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How good are you at finding the formula for a number pattern ?

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Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . .

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Can you find rectangles where the value of the area is the same as the value of the perimeter?

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Can you find a rule which connects consecutive triangular numbers?

This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.

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Can you find a rule which relates triangular numbers to square numbers?

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Here are three 'tricks' to amaze your friends. But the really clever trick is explaining to them why these 'tricks' are maths not magic. Like all good magicians, you should practice by trying. . . .

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Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

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Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

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Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?

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Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

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Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?

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Can you see how to build a harmonic triangle? Can you work out the next two rows?

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Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

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When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

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Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

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Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

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We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

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Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

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I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...

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The Number Jumbler can always work out your chosen symbol. Can you work out how?

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How many winning lines can you make in a three-dimensional version of noughts and crosses?

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The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?

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Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

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Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

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Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

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Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. . . .

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Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel. . . .

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The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 ï¿½ 1 [1/3]. What other numbers have the sum equal to the product and can this be. . . .

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Where should you start, if you want to finish back where you started?

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A job needs three men but in fact six people do it. When it is finished they are all paid the same. How much was paid in total, and much does each man get if the money is shared as Fred suggests?

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List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?