# Problem 334: Spilling the beans
In Plato's heaven, there exist an infinite number of bowls in a straight
line. Each bowl either contains some or none of a finite number of
beans. A child plays a game, which allows only one kind of move:
removing two beans from any bowl, and putting one in each of the two
adjacent bowls. The game ends when each bowl contains either one or no
beans. For example, consider two adjacent bowls containing 2 and 3 beans
respectively, all other bowls being empty. The following eight moves
will finish the game: You are given the following sequences: t0 =
123456. ti = ti-12 , if ti-1 is even ti-12 926252, if ti-1 is odd where
⌊x⌋ is the floor function and is the bitwise XOR operator. bi = ( ti mod
211) + 1. The first two terms of the last sequence are b1 = 289 and b2 =
145. If we start with b1 and b2 beans in two adjacent bowls, 3419100
moves would be required to finish the game. Consider now 1500 adjacent
bowls containing b1, b2,..., b1500 beans respectively, all other bowls
being empty. Find how many moves it takes before the game ends.