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Helen's Conjecture

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

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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?

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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?

Where Can We Visit?

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2
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?