Fabulous response for the puzzle…one of the best weeks since I started the puzzle blog two years back…thanks and keep puzzling.

I got three correct answers (of course other than Vaibhav Kalia who had contributed the puzzle). The answer is “I am Martin”. The best way to explain the answer came from Anubhav Garg, which I am reproducing here:

Working:

Note that x is the same as 4x/4, which means that the three people Walter, Martin and Steve should have initial amounts in the ratio of 3:5:4…which will mean that if I have 50 cents, I must be Martin.

Some people misunderstood the variation – what I had meant was that all three come back to the position they started from. You can figure out the answer with a little bit of trial and error that the three will have starting coins in the ratio of 1:2:2, and that the cycle can continue endlessly. Since Steve and Martin have coins that are a multiple of 2, in this case I must be Walter!

Hope you enjoyed the puzzle.