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?
Will they be able to visit every number on the grid at least once?
What would have happened if they had started on a different number?
Can you explain your results?