What is the maximum possible number of streets any one of which could be the one the crew cleaned on Friday afternoon?

lexiw September 5, 2020

The 8th spot was already accounted for the Monday afternoon slot. So that leaves us with the options of 2 and 5 in the Friday slot. We do not have a definite relationship for 1,3, and 6 so therefore those options can go into the Friday slot as well. That leaves us with the options: 2,5,1,3, and 6. I know I am not a tutor so I really hope that helps!! I think you just forgot to take into account that 8 was already delegated to slot Monday and that just because 2,5, and 8 HAVE to go into the afternoons this does not mean that 1,3, and six cannot go into the afternoons because we don't know the exact relationships in this instance.

Victoria September 16, 2020

Hi @ritagentile and @lexiw,

@lexiw, you are absolutely correct! Great to see that you're getting the concepts and engaging with other students on the message boards.

We know that Eighth Street must be cleaned on Monday afternoon because Rule 6 tells us that Eighth Street is cleaned on an afternoon and Rule 5 tells us that Fourth Street was cleaned after Eighth Street. Fourth Street was cleaned Tuesday morning; the only afternoon slot prior to this is Monday afternoon.

Rule 6 tells us that Second and Fifth street must be cleaned on afternoons. Therefore, it is entirely possible that either of these streets were cleaned Friday afternoon.

We know that Sixth Street must be cleaned after Fourth Street and we know nothing about First and Third Street. It is possible that any one of these streets was cleaned Friday afternoon as demonstrated by the three possibilities I've outlined below.

Option 1 - First Street cleaned Friday afternoon

3 4 6 7 X
8 5 X 2 1
M T W R F

Option 2 - Third Street cleaned Friday afternoon

1 4 6 7 X
8 5 X 2 3
M T W R F

Option 3 - Sixth Street cleaned Friday afternoon

1 4 3 7 X
8 5 X 2 6
M T W R F

Therefore, there are five possible streets which could be cleaned Friday afternoon: 1, 2, 3, 5, and 6.

Keep up the great work both of you and please let us know if you have any further questions!

Nikhi May 8, 2021

Hi, so just to confirm, since the question did not state the exact relationship for 1st, 3rd, 6th street, we cannot just assume it stays in the mornings right? Because I thought only 2nd, 5th, 8th street can go in the afternoons, leaving those the only options?

jilliansarro November 5, 2021

I don't see how 1st or 3rd street are options when we are trying to fill an afternoon slot and there are only 3 afternoon options (2,5,8).