There are definitely some values that don't fit that criterion

No I just double checked. You may be falling for an optional illusion where the line dips down for a value and then spikes up and the line due to rendering issues doesnt ever actually touch the data point. Also fine there are enough points where the condition holds that the student is probably fabricating numbers.

Well no - look at the second-lowest point that yellow reaches - whatever that is, it's $2.5 < x < 5$

@question Looks like 2.5 to me.

I mean, there are no values, and there's no indication of the level of precision, so we can't possibly make that judgment

Remember that the professor only needs probable cause to call in the student not smoking gun evidence so some approximation is fine

@BenjaminBraun So... you know for a fact that all the values are multiples of 2.5, but also are going entirely on approximation? In that case, why not say that all of (e.g.,) red's values 'approximate' to an integer?

Because it is unnecessary

@BenjaminBraun lol what.

The professor is alleging that the values are exactly multiples of 2.5, his observation is based on them looking approximately to be multiples of 2.5. The meaning of the allegation changes if I put the word approximately in the answer.

@BenjaminBraun But nobody is alleging that - you can't justify an answer with criteria that you invented out of whole cloth. And again, it stands that you could say the same thing about any of the other answers, based on the amount of information available to us.

I am alleging that in the place of the professor, and no the other two lines don't appear to have this property at all

Again, you can't allege information about a puzzle to justify your answer. You have to be able to justify your answer with information that is actually in the puzzle. And yes, you can absolutely say that red (or blue)'s points all "look like" integer values with no more or less arbitrariness than your allegation

Occasms razor, and also again my answer was why the professor calls the student in, which is the values are multiples of 2.5, the processor determines this since it looks that way. I could have my answer have three sections, answer, why, and why that why, but that feels too pedantic

but we don't know what the values actually are

also, the person who deleted their answer did not necessarily have the right answer (though I upvoted it too)

Looks like F has an even better one

I mean that's like a rebus puzzle someone posts a picture of a cat and you are saying 'we can't be sure that's a cat!"

no

it's not like that at all

Because?

because there's no analogue to a cat for the difference between (say) 1 and 1.0536

we have no way of knowing what the actual values on the chart are, unless they are explicitly provided in the puzzle

Fair enough about the cat

The professor is observing a pattern and acting on that pattern. He's probably not wrong about the pattern.

but you're guessing at the existence of that pattern

you're adding information that isn't in the puzzle

It's possible the actual pattern is multiples of 2.5 plus epsilon

don't get me wrong - were this a real life situation, I wouldn't fault a professor for acting on that

but... it's a puzzle that should be solvable with the information we have

once we start making the determination that the precise data shows a pattern, we're introducing information that we just made up in our heads.

No the information is there a pattern of roughly multiples of 2.5. If you can observe a patten and its roughly a fit to your observation you can propose the answer

This puzzle doesn't need to be uniquely solvable by a machine it's intended to be explored creatively

no, the information is not there

Fs answer can also not be verified exactly

the only values that exist at all are along the y axis

yes, I agree

You're requirements are needlessly strict

Lighten up

These are for fun

lol

lmao