[stevesimmons]

I solved this in a hedge fund interview with "Consider the limiting case of a coin the same size as the table... You can only place it at the centre, and you win... Now make the coin smaller. How does the strategy change?... It can't, because of symmetry."

They didn't consider it a valid solution :|

[fenomas]

This solution doesn't hold - just because a game is symmetrical, doesn't guarantee that the optimal move in some limiting case works in all cases.

For example, consider if the game was played with N>2 players, or if the win condition was to make the first move modulo N, for some N>2. In those cases everything would still be symmetrical, and playing in the center would still be a winning move for huge coins, but not (necessarily) for smaller coins.

[petters]

It is not clear to me how to play following your strategy. There are things missing. You need to describe what the second move should look like.

[toxik]

Well, that explanation is a total cop out, so I can see why they would think that.

[Y_Y]

I disagree. Arguments to symmetry like this are found all over the place, especially in the kind of geometry and physics I'm familiar with. In fact the solution I came up with when I read the problem was very similar.

[quietbritishjim]

The original comment (by tasty_freeze) was an argument to symmetry. Just saying "because of symmetry" is not a proper explanation.

[Y_Y]

You're right that it's not a proper explanation. This feels just like a case of "details are left as an exercise". This is most frustrating when you're learning a subject, and you want to be able to check the details, or you are skeptical of a claim. Inevitably though people elide things that they think the reader (who they model as similar to themselves) will immediately be able to guess based on their experience. I'm sure you can think of an equivalent situation in your field of expertise.

[quietbritishjim]

I can think of things where I would leave out details that a non-expert would need filled in. Except, I wouldn't do that in an interview situation where someone is specifically asking me to explain that one thing. (Yes they started with the giant coin thing, but "symmetry" is still the substantial majority of their argument.)

The sibling to my first comment says it a lot better than I did: in a similar but different situation there's symmetry but no analogous strategy, so further explanation really is needed here.

In a sense, that makes it even more damning. Eliding details that you don't realise are important, but actually are, shows a real lack of understanding of your own argument. And that's something I have definitely witnessed in my own field!

[Y_Y]

Oh man, I assumed he explained it in the interview and was just leaving out the details for the purposes of the comment. That was me being dense.