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?
Does it make a difference if the other coin is 1 more or 2 more than a multiple of 3z? (or 5z or 7z...)
The whole class introductory activity as described above should provide the necessary support for all students to access this problem.