Advent of Code

--- Day 9: Marble Mania ---

   You talk to the Elves while you wait for your navigation system to
   initialize. To pass the time, they introduce you to their favorite marble
   game.

   The Elves play this game by taking turns arranging the marbles in a
   circle according to very particular rules. The marbles are numbered
   starting with 0 and increasing by 1 until every marble has a number.

   First, the marble numbered 0 is placed in the circle. At this point,
   while it contains only a single marble, it is still a circle: the marble
   is both clockwise from itself and counter-clockwise from itself. This
   marble is designated the current marble.

   Then, each Elf takes a turn placing the lowest-numbered remaining marble
   into the circle between the marbles that are 1 and 2 marbles clockwise of
   the current marble. (When the circle is large enough, this means that
   there is one marble between the marble that was just placed and the
   current marble.) The marble that was just placed then becomes the current
   marble.

   However, if the marble that is about to be placed has a number which is a
   multiple of 23, something entirely different happens. First, the current
   player keeps the marble they would have placed, adding it to their score.
   In addition, the marble 7 marbles counter-clockwise from the current
   marble is removed from the circle and also added to the current player's
   score. The marble located immediately clockwise of the marble that was
   removed becomes the new current marble.

   For example, suppose there are 9 players. After the marble with value 0
   is placed in the middle, each player (shown in square brackets) takes a
   turn. The result of each of those turns would produce circles of marbles
   like this, where clockwise is to the right and the resulting current
   marble is in parentheses:

 [-] (0)
 [1]  0 (1)
 [2]  0 (2) 1
 [3]  0  2  1 (3)
 [4]  0 (4) 2  1  3
 [5]  0  4  2 (5) 1  3
 [6]  0  4  2  5  1 (6) 3
 [7]  0  4  2  5  1  6  3 (7)
 [8]  0 (8) 4  2  5  1  6  3  7
 [9]  0  8  4 (9) 2  5  1  6  3  7
 [1]  0  8  4  9  2(10) 5  1  6  3  7
 [2]  0  8  4  9  2 10  5(11) 1  6  3  7
 [3]  0  8  4  9  2 10  5 11  1(12) 6  3  7
 [4]  0  8  4  9  2 10  5 11  1 12  6(13) 3  7
 [5]  0  8  4  9  2 10  5 11  1 12  6 13  3(14) 7
 [6]  0  8  4  9  2 10  5 11  1 12  6 13  3 14  7(15)
 [7]  0(16) 8  4  9  2 10  5 11  1 12  6 13  3 14  7 15
 [8]  0 16  8(17) 4  9  2 10  5 11  1 12  6 13  3 14  7 15
 [9]  0 16  8 17  4(18) 9  2 10  5 11  1 12  6 13  3 14  7 15
 [1]  0 16  8 17  4 18  9(19) 2 10  5 11  1 12  6 13  3 14  7 15
 [2]  0 16  8 17  4 18  9 19  2(20)10  5 11  1 12  6 13  3 14  7 15
 [3]  0 16  8 17  4 18  9 19  2 20 10(21) 5 11  1 12  6 13  3 14  7 15
 [4]  0 16  8 17  4 18  9 19  2 20 10 21  5(22)11  1 12  6 13  3 14  7 15
 [5]  0 16  8 17  4 18(19) 2 20 10 21  5 22 11  1 12  6 13  3 14  7 15
 [6]  0 16  8 17  4 18 19  2(24)20 10 21  5 22 11  1 12  6 13  3 14  7 15
 [7]  0 16  8 17  4 18 19  2 24 20(25)10 21  5 22 11  1 12  6 13  3 14  7 15

   The goal is to be the player with the highest score after the last marble
   is used up. Assuming the example above ends after the marble numbered 25,
   the winning score is 23+9=32 (because player 5 kept marble 23 and removed
   marble 9, while no other player got any points in this very short example
   game).

   Here are a few more examples:

     * 10 players; last marble is worth 1618 points: high score is 8317
     * 13 players; last marble is worth 7999 points: high score is 146373
     * 17 players; last marble is worth 1104 points: high score is 2764
     * 21 players; last marble is worth 6111 points: high score is 54718
     * 30 players; last marble is worth 5807 points: high score is 37305

   What is the winning Elf's score?

   Your puzzle answer was 394486.

--- Part Two ---

   Amused by the speed of your answer, the Elves are curious:

   What would the new winning Elf's score be if the number of the last
   marble were 100 times larger?

   Your puzzle answer was 3276488008.

   Both parts of this puzzle are complete! They provide two gold stars: **

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