Full Solution - Run my Code
Days Comments: Spent longer than I'd like to admit rewriting my code so that it works recursively.
Part One: List Comparisons - Original Puzzle
You find a pile of scratchcards. Each scratchcard has two lists of numbers: a list of winning numbers and a list of your numbers. The goal is to count the points, where the first match earns 1 point, and subsequent matches double the point value.
Example:
Card 1: 41 48 83 86 17 | 83 86 6 31 17 9 48 53
Card 2: 13 32 20 16 61 | 61 30 68 82 17 32 24 19
Card 3: 1 21 53 59 44 | 69 82 63 72 16 21 14 1
Card 4: 41 92 73 84 69 | 59 84 76 51 58 5 54 83
Card 5: 87 83 26 28 32 | 88 30 70 12 93 22 82 36
Card 6: 31 18 13 56 72 | 74 77 10 23 35 67 36 11
Card 1 has five winning numbers - 41, 48, 83, 86, and 17
and the eight numbers you have - 83, 86, 6, 31, 17, 9, 48, and 53.
Four of your numbers, 48, 83, 17, and 86 are winning numbers!
-That means Card 1 is worth 8 points (1 for the first match, then doubled three times for each of the three matches after the first).
-Card 2 - two winning numbers (32 and 61), worth 2 points.
-Card 3 - two winning numbers (1 and 21), worth 2 points.
-Card 4 - one winning number (84), worth 1 point.
-Card 5 - no winning numbers, worth no points.
-Card 6 - no winning numbers, worth no points.
This pile of scratchcards is worth 13 points.
Look at the larger pile of scratchcards. How many points are they worth in total?
Part Two: Recursive Functions - Original Puzzle
Upon realizing that the rules are printed on the back of each card, you discover there are no such thing as points! Instead, winning scratchcards grants you more scratchcards equal to the number of winning numbers you have.
Specifically, you win copies of the scratchcards below the winning card equal to the number of matches.
So, if card 10 were to have 5 matching numbers, you would win one copy each of cards 11, 12, 13, 14, and 15.
The process repeats until no more scratchcards are won.
Example:
Card 1: 41 48 83 86 17 | 83 86 6 31 17 9 48 53
Card 2: 13 32 20 16 61 | 61 30 68 82 17 32 24 19
Card 3: 1 21 53 59 44 | 69 82 63 72 16 21 14 1
Card 4: 41 92 73 84 69 | 59 84 76 51 58 5 54 83
Card 5: 87 83 26 28 32 | 88 30 70 12 93 22 82 36
Card 6: 31 18 13 56 72 | 74 77 10 23 35 67 36 11
Card 1 has four matches, so you win one copy each of the next four cards: Cards 2, 3, 4, and 5.
Your original Card 2 has two matching numbers, so you win one copy each of Cards 3 and 4.
Your copy of Card 2 also wins one copy each of Cards 3 and 4.
Your four instances of Card 3 (one original and three copies) have two matching numbers, so you win four copies each of Cards 4 and 5.
Your eight instances of Card 4 (one original and seven copies) have one matching number, so you win eight copies of Card 5.
Your fourteen instances of Card 5 (one original and thirteen copies) have no matching numbers and win no more cards.
Your one instance of Card 6 (one original) has no matching numbers and wins no more cards.
Once all of the originals and copies have been processed, you end up with:
-1 instance of Card 1
-2 instances of Card 2
-4 instances of Card 3
-8 instances of Card 4
-14 instances of Card 5 and
-1 instance of Card 6
In total, this example pile of scratchcards causes you to ultimately have 30 scratchcards!
Process all of the original and copied scratchcards until no more scratchcards are won. How many total scratchcards do you end up with?