Problem 882: Removing Bits
Dr. One and Dr. Zero are playing the following partisan game.
The game begins with one
Dr. One chooses a number and changes it by removing a
Dr. Zero chooses a number and changes it by removing a
The player that is unable to move loses.
Note that leading zeros are not allowed in any binary expansion; in particular
nobody can make a move on the number
They soon realize that Dr. Zero can never win the game. In order to make it more interesting, Dr. Zero is allowed to "skip the turn" several times, i.e. passing the turn back to Dr. One without making a move.
For example, when
Let
For example,
Find