adventofcode/2016/day15/problem

Advent of Code

--- Day 15: Timing is Everything ---

   The halls open into an interior plaza containing a large kinetic sculpture.
   The sculpture is in a sealed enclosure and seems to involve a set of
   identical spherical capsules that are carried to the top and allowed to
   bounce through the maze of spinning pieces.

   Part of the sculpture is even interactive! When a button is pressed, a
   capsule is dropped and tries to fall through slots in a set of rotating
   discs to finally go through a little hole at the bottom and come out of the
   sculpture. If any of the slots aren't aligned with the capsule as it passes,
   the capsule bounces off the disc and soars away. You feel compelled to get
   one of those capsules.

   The discs pause their motion each second and come in different sizes; they
   seem to each have a fixed number of positions at which they stop. You decide
   to call the position with the slot 0, and count up for each position it
   reaches next.

   Furthermore, the discs are spaced out so that after you push the button, one
   second elapses before the first disc is reached, and one second elapses as
   the capsule passes from one disk to the one below it. So, if you push the
   button at time=100, then the capsule reaches the top disc at time=101, the
   second disc at time=102, the third disc at time=103, and so on.

   The button will only drop a capsule at an integer time - no fractional
   seconds allowed.

   For example, at time=0, suppose you see the following arrangement:

 Disc #1 has 5 positions; at time=0, it is at position 4.
 Disc #2 has 2 positions; at time=0, it is at position 1.

   If you press the button exactly at time=0, the capsule would start to fall;
   it would reach the first disc at time=1. Since the first disc was at
   position 4 at time=0, by time=1 it has ticked one position forward. As a
   five-position disc, the next position is 0, and the capsule falls through
   the slot.

   Then, at time=2, the capsule reaches the second disc. The second disc has
   ticked forward two positions at this point: it started at position 1, then
   continued to position 0, and finally ended up at position 1 again. Because
   there's only a slot at position 0, the capsule bounces away.

   If, however, you wait until time=5 to push the button, then when the capsule
   reaches each disc, the first disc will have ticked forward 5+1 = 6 times (to
   position 0), and the second disc will have ticked forward 5+2 = 7 times
   (also to position 0). In this case, the capsule would fall through the discs
   and come out of the machine.

   However, your situation has more than two discs; you've noted their
   positions in your puzzle input. What is the first time you can press the
   button to get a capsule?

   Your puzzle answer was 400589.

--- Part Two ---

   After getting the first capsule (it contained a star! what great fortune!),
   the machine detects your success and begins to rearrange itself.

   When it's done, the discs are back in their original configuration as if it
   were time=0 again, but a new disc with 11 positions and starting at position
   0 has appeared exactly one second below the previously-bottom disc.

   With this new disc, and counting again starting from time=0 with the
   configuration in your puzzle input, what is the first time you can press the
   button to get another capsule?

   Although it hasn't changed, you can still get your puzzle input.

   Answer: 3045959

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