This was indeed a beautiful puzzle, thanks again Prateek! Apologies that I could not post anything last weekend, I was traveling.
I got correct answers from Suman Saraf, Pratik Poddar and Shruti Mittal – well done all.
Reproducing the answer from Pratik Poddar here:
“I play first. I place my first coin at the centre of the table. Then the other guy places somewhere. My response is always to place a coin at the exact diamaterical opposite point. Hence I always have a way to put the coin if he has. I win.”
Hope you all enjoyed the puzzle!