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Take three consecutive numbers and add them together. What do you notice?

Challenge Level

How many sets of three consecutive odd numbers can you find, in which all three numbers are prime?

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What can we say about all the primes which are greater than 3?

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Is there a quick and easy way to calculate the sum of the first 100 odd numbers?

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Take four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Challenge Level

If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?

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Which numbers cannot be written as the sum of two or more consecutive numbers?

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$40$ can be written as $7^2 - 3^2.$ Which other numbers can be written as the difference of squares of odd numbers?

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Can you work through these direct proofs, using our interactive proof sorters?

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Here are a few questions taken from the Test of Mathematics for University Admission (or TMUA).

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These secondary problems have not yet been solved. Can you be the first?