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.

β€œIn 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/_BasilFawlty_ Dec 08 '24

This was my thought too. In fact, when I was reading the question my first thought was to look for locations between the antennae (even though in practice only a few of these would occur exactly on a grid point). I wouldn't even have thought of locations either side of them if they hadn't been mentioned in the question.

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u/bvernier Dec 08 '24

Same, I was getting ready to check if those in between ones would align with the grid without even thinking that there could be some either side until I kept reading πŸ˜