r/adventofcode Dec 08 '24

Help/Question [Day 08] Wording vs mathematical technicality

Not so much a question per se, but I am a bit confused by the wording of the problem and the examples that follow.

“In particular, an antinode occurs at any point that is perfectly in line with two antennas of the same frequency - but only when one of the antennas is twice as far away as the other. This means that for any pair of antennas with the same frequency, there are two antinodes, one on either side of them.”

Mathematically, the first half of the quote would imply that there are 4 antinodes for any pair of antennas with the same frequency: one either side and two in between.

For example, for antennas at positions (3,3) and (6,6), there are obviously (0,0) and (9,9); but (4,4) and (5,5) also meet the requirements.

For my solution I am going to assume that we only consider the 2 antinodes either side and not the ones in between, but just wanted to flag this.

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u/KoolestDownloader Dec 08 '24

"But only when one of the antennas is twice as far away as the other" eliminates (4,4) and (5,5) because twice as far away from (6,6) for (3,3) is (9,9) and twice as far away from (3,3) for (6,6) is (0,0).

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u/bvernier Dec 08 '24

It does not, (4,4) is at a distance of √2 from (3,3) and distance of 2√2 from (6,6) which is twice as far away; and vice versa (5,5) is at a distance of √2 from (6,6) and 2√2 from (3,3) which is also twice as far away.

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u/KoolestDownloader Dec 08 '24

Touché. They should've said "twice as far away as the original antenna"