Which one of the following is an acceptable evaluation schedule, with the textbooks listed in order of evaluation fro...

Irina November 10, 2019

@maonuo,

Let's look at the setup for this game. We have six books - 3 intro books - F G H, and 3 advanced - XYZ that each must be evaluated by the editor - J and publisher - R during six consecutive weeks. No textbooks is evaluated by J and R during the same week.

J: __ __ __ __ __ __
R: __ __ __ __ __ __

The following rules apply:
(1) R cannot evaluate any intro textbook until J has evaluated that textbook.

This rule tells us that R must evaluate an advanced book - X Y Z - in week #1 because the earliest he could evaluate one of the intro textbooks is week 2 assuming J evaluates one of the intro textbooks in week 1. This rule also tells us that J must evaluate an advanced textbook - X Y Z in week #6 because R must evaluate any intro textbooks after J.

(2) J cannot evaluate an advanced textbook until R has evaluated that textbook.

This rule tells us that J cannot evaluate an advanced textbook in week 1, thus he must evaluate an intro textbook in week #1 - F G H. This rule also allows us to infer that R must evaluate an intro textbook in week #6. Let's put these inferences on the diagram:

J: I __ __ __ __ A
R: A __ __ __ __I

(3) R cannot evaluate any intro books consecutively.

This rule allows us to conclude that R's book #5 must be advanced since #6 is intro, and that R must evaluate intro books in weeks #2 and #4 and an advanced book in week #5.

J: I __ __ __ __ A
R: A I A I A I

(4) J must evaluate X during week 4.

J: I __ __ X __ A
R: A I A I A I

If J evaluates X - an advanced - during week 4, R must evaluate X in either weeks 1 or 3 per rule 2. This rule also allows us to conclude that book #6 by J and book #5 by R must be the same. The reason for this inference is because J must evaluate any advanced book after R per rule 2, any scenario would result in this pair of books being the same. Since we know that X -X pair must in weeks 1-4 or 3-4, let's consider the possible placement of Y and Z:

J: I 2 3 X Y Z
R: X/Y I X/Y I Z I

In this scenario, if J evaluate Z #6 and Y #5, R must evaluate Z #5 because Y must be evaluated in a prior week.

J: I Y 3 X 5 Z
R: Y I X I Z I


J: I 2 Y X 5 Z
R: Y I X I Z I

We can see that in all possible scenarios, the last advanced pair #6 - J and #5- R must be the same and could either be X or Z.

J: I __ __ X __ Y/Z
R: A I A I Y/Z I

We can further infer that J must review at least two intro textbooks in weeks 1-3, resulting in three possible scenarios:

(1) J: I A I X I Y/Z
R: A I A I Y/Z I

(2) J: I I I X A Y/Z
R: A I A I Y/Z I

(3) J: I I A X I Y/Z
R: A I A I Y/Z I

Note that in every scenario, J book #1 and R book #2 must be intro books, and since R can only review an intro book after J, they must necessarily be the same book.

J#1 = R#2.

Let me know if this helps and if you have any further questions.