2015 pieces of stones are placed to form a circle. They are numbered with 1,2,3,4,...,2015 clockwise. Starting from somewhere, you remove a stone. Then going clockwise, you remove every other stone, one at a time. Finally, there is only stone left, and that stone is 2014. What was the first stone you removed?
Perhaps it is easier to focus on what remains after each round of eliminations?
Start with eliminating 1.
After half the numbers are eliminated, what is left is of the form 2n.
After two rounds, what is left is of the form 4n + 2.
Then what is left is 8n + 6
Then 16n + 14
Then 32n + 30
Then 64n + 62
Then 128n + 62
Then 256n + 190
Then 512n + 446
Then 1024n + 958
This can only be 1982.
Then the starting point = 1 + (2014 - 1982) = 33
Analytic Approach ?
