Coursebook chapter 4 page 4-32, Game 1, February 92

[Lina]

Hi, I am reviewing game 1, February 92, and need help understanding question #16

In general, I dont know how to go about tackling this question type, where I must find the maximum and minimum arrangements. If you can give me some guidance on how to approach this question that would be helpful, as well as specific guidance to this question on the maximum number of different schedules.

Are there explanations I can refer to for this section? I only have access to chapter 4 HW explanations. Also, which chapter in the coursebooks and LGB can I refer to review this question type?

Thanks!

[Lucas Moreau]

When it talks about "maximum and minimum arrangements", what it is asking is how many possible combinations are present given the Local restriction - what is the most, maximum, number of ways that the streets could be cleaned while laboring under the given conditions.

In this case, due to the initial setup of the game, we know that Seventh Street will be cleaned on Thursday AM. Since the placements of Monday PM, Tuesday AM, and Wednesday PM are all determined, and Monday AM is set to be either First or Third Street, in order for Fifth, Sixth, and Seventh Streets to be cleaned in numerical order, Fifth Street would have to be cleaned on Tuesday PM and Sixth Street on Wednesday AM. Those are the only possible spaces for Fifth and Sixth Street to occupy.

Given this, the only spaces left with any uncertainty are Monday AM, Thursday PM, and Friday PM, and the only streets left are First, Second, and Third Streets. This leaves us with only four possible combinations:

M(AM) 1, Th(PM) 2, F(PM) 3
M(AM) 1, Th(PM) 3, F(PM) 2
M(AM) 3, Th(PM) 2, F(PM) 1
M(AM) 3, Th(PM) 1, F(PM) 2

As such, with 5-6-7 determined, we know there are but four possible combinations, and that is the maximum number of combinations extant. Let me know if you have any more questions.

Hope that helps,
Lucas Moreau
PowerScore

[Lina]

Thanks! Can you clarify the part of the stimulus that says, "It takes an entire crew an entire morning or an entire afternoon to clean a street" I interpreted the OR as, the crew either cleans in the AM or PM but not both.

[Steve Stein]

Hi Lina,

You interpreted that correctly--it takes either a whole morning, or a whole afternoon, but not both.

~Steve