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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?

How Much Can We Spend?

Stage: 3 Challenge Level: Challenge Level:1

8z (3+5)
9z (3+3+3)
10z (5+5)
11z (3+3+5)
12z (3+3+3+3)
13z (3+5+5)
14z (3+3+3+5)...

What do you notice about 8z, 11z, 14z......?