The Elves contact you over a highly secure emergency channel. Back at the North Pole, the Elves are busy misunderstanding White Elephant parties.
Each Elf brings a present. They all sit in a circle, numbered starting with position 1. Then, starting with the first Elf, they take turns stealing all the presents from the Elf to their left. An Elf with no presents is removed from the circle and does not take turns.
For example, with five Elves (numbered 1 to 5):
1 5 2 4 3
- Elf 1 takes Elf 2's present.
- Elf 2 has no presents and is skipped.
- Elf 3 takes Elf 4's present.
- Elf 4 has no presents and is also skipped.
- Elf 5 takes Elf 1's two presents.
- Neither Elf 1 nor Elf 2 have any presents, so both are skipped.
- Elf 3 takes Elf 5's three presents.
So, with five Elves, the Elf that sits starting in position 3 gets all the presents.
With the number of Elves given in your puzzle input, which Elf gets all the presents?
Ensure you have the Mercury compiler mmc on your machine, then
make
This… took a bit more work than I anticipated. Turns out logic programming with extra restrictions is extra hard!
The approach is simple: simulate traversal of a circular list, and keep passing the presents from one to the next in succession until there is one left. Took a while to get determinism qualifiers/checks in place, but eventually got it.
Now for the juicy part. To even do this in the naive way (which, let's be real, I'm going to try) you need a much more general/programmable circular list (before I was just embedding the "cicularness" in the clauses.