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Count down to Christmas with maths!

Where do the magnetic fields of planets and stars come from?

- In this podcast Paul Shepherd tells us about the maths of football stadiums and why his work required him to listen to Belgian techno.
Amidst all the controversy of the FIFA World Cup 2022 there is also some football to be played. And where there's football, there's maths...

Tosin uses maths to guarantee the continued production of chocolate.

Please help :-)

I have tried to find out the possible configurations with only two marbles left and I am finding that the number of those is quite larger than the five possibilities with only one marble left.

The article author writes that "finishing with two marbles might be a little bit, but not much, easier than finishing with one", which is not very precise.

My argument is based on the fact that the last two marbles left should occupy holes labeled "f" and "g" and then I start discarding possibilities based on the symmetry of the board. For example all the "f" and "g" holes that are converted into "h" by a symmetry will be discarded.

But I still get too many to agree with the author's words (sorry for not giving the total number in my count. I stopped the counting when I realized something must have been wrong).

Thank you,

Marcos