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Sinead has $10$ pockets and $44$ one pound coins.
She wants to put all these pounds into her pockets so that each pocket contains a different number of coins.
Prove that this is impossible.
What is the minimum number of coins Sinead would need in order to be able to do this?
I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?
I start with a red, a blue, a green and a yellow marble. I can trade any of my marbles for three others, one of each colour. Can I end up with exactly two marbles of each colour?
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?