My thought would be to "solve" the problem for a 2x2 table (easy -- put it anywhere), a 3x3 (put it in the **middle**), a 4x4, 5x5, etc. Hopefully, a pattern will emerge and become a universal strategy.

Oh?

Hmm, I was assuming a grid, but now that I re-read the question, I see that there isn't one.

But, to completely answer your original question:

Yes.

You're right But you must prove it. Don't be daunted by the word "prove", though. Think of it as coming up with an argument that no one can deny. The best way to prove it in this case, and in many problems like this, is to come up with an algorithm for winning, i.e. an algorithm (strategy) that guarantees that the first player to move wins.

You didn't say that! You just asked a yes/no question, and I gave the correct answer based on meta-data. Basically, you wouldn't have asked this if the question was no.

But actually, I think based on your hint that I see the answer.

1) Place you first penny in the exact center

2) Place your second, third, etc. penny exactly on the opposite side of the table. By definition, there won't be a penny there.

Eventually, there will be nowhere left to go for player 2.

What do I win?