Square numbers

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Favourite

Square Subtraction

Age

7 to 11

Challenge level

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
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Picturing Square Numbers

Age

11 to 14

Challenge level

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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Sticky Numbers

Age

11 to 14

Challenge level

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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Favourite

Factors and Multiples Puzzle

Age

11 to 14

Challenge level

Using your knowledge of the properties of numbers, can you fill all the squares on the board?
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Favourite

Generating Triples

Age

14 to 16

Challenge level

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
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Favourite

Odd Differences

Age

14 to 16

Challenge level

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.
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Favourite

Filling the Gaps

Age

14 to 16

Challenge level

Which numbers can we write as a sum of square numbers?
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Favourite

Iff

Age

14 to 18

Challenge level

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
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Pythagorean Quadruple

Age

14 to 16

Challenge level

The sum of three square numbers equals $121$. What can those numbers be...
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Time of Birth

Age

11 to 14

Challenge level

A woman was born in a year that was a square number, lived a square number of years and died in a year that was also a square number. When was she born?