Which one of the following could be an accurate assignment of students, in order from the earliest year to the latest?

shunhe on August 19, 2020

Hi @BrundonDavey,

Thanks for the question! So we have four students here searching archives from 1921-1924. Sounds like the years are a good way to sort it, and each year only has one student. But we also have 6 total students, and only four of them can be picked. So 2 students are going to be out as well, and that’s also something we should keep track of. So I would draw something like this

__ __ __ __ | __ __

Where the slots on the left of the vertical line are for the years, and the slots on the right are for the students who aren’t picked.

Now we can diagram the rules. Only L or T can be in 1923, so we can put “L/T” in slot 3. If M is in, she’s in 1921 or 1922, so

M —> 21 v 22

If T is in, then R is in, so

T —> R
~R —> ~T

And if R is in, then O is right before R, so

R —> OR

Which also means that R can’t be in 1921, so that’s something we can note as well with a ~R below 1921. R also can’t be in 1924, since that would put O in 1923, but only L or T can go in 1923. And obviously, R can’t go in 3. So R, if it’s in the game, has to go in slot 2. Which means that O would be in slot 1, which means that M can’t be in the game. So if R is in the game, M can’t be in the game. And if M is in the game, then R can’t be in the game. But also, they can’t both be out of the game, since if they’re both out, T also has to be out, but that means we took 3 people out, and we can only take 2 people out. Also, speaking of T, when T is in, it can’t be in slots 1 and 2, because R will be in and have to go in slot 2, and O will go in slot 1. So T can only be in slots 3 and 4. Those are some of the inferences you can make up front.

Hope this helps! Feel free to ask any other questions that you might have.

BrundonDavey on September 2, 2020

Super response! Thank you for the thoroughness!