Thanks for the question! So being asked to determine, for a truck, exactly how many trucks arrived before it, is basically asking which slot it’s in, right? Because it we know exactly how many trucks came before a truck, we know what slot that truck is in. So the question is basically asking us, which trucks can we place for sure.
So we know S is the sixth truck, so that’s one of them. Can we place any others for sure? Well, we know from rule 2 that Y comes before T and W, which would normally imply that Y is at earliest fifth. But actually, we know that S is in sixth. So T and W, even if they’re both as late as possible, mean that Y can be at latest 4th.
Now what else do we know. We know two trucks before Y are red, and no two consecutive arrivals are red. That means at least three trucks come before Y. That means Y is at earliest fourth.
But now we know that Y is at latest fourth and at earliest fourth. That means . . . Y is fourth. So we can place both Y and S, but none of the others. So that means we can place two trucks for sure, meaning we know exactly how many trucks come before these trucks. So the answer is two.
Hope this helps! Feel free to ask any other questions that you might have.
c0cald01on July 16, 2021
Why wouldn't we know about four? Being that Y is 4th and S is 6th but W could be 5th and T could be 7th. Is it because W and T could change places and this is a must be true question?
Emil-Kunkinon November 20 at 01:38PM
It's exactly because W and T can change places, and this is a must be true!
