Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
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?
We define "strange" numbers in the following way:
Find all strange numbers.
This problem comes from the Hungarian magazine KoMaL. You can find many other challenging problems in English on the KoMaL website.