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Age 11 to 14
Challenge Level 
What happens to multiples of 5 when they are doubled?
What about numbers that are 1 more, 2 more, 3 more and 4 more than a multiple of 5?
What happens to multiples of 5 when 5 is subtracted from them?
What about numbers that are 1 more, 2 more, 3 more and 4 more than a multiple of 5?
What about numbers that are 1 more, 2 more, 3 more and 4 more than a multiple of 5?
What happens to multiples of 5 when 5 is subtracted from them?
What about numbers that are 1 more, 2 more, 3 more and 4 more than a multiple of 5?
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Marbles
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?
More Marbles
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?
Differences
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?