- Thu Aug 06, 2020 2:02 pm
#77787
Hi mollyquillin!
In diagramming this one out, it seems to me that it's especially important to make sure to include all of the not-laws in the original diagram.
In fact, there were enough not-laws under Wednesday and Saturday that it seemed worthwhile to list the possibilities of variables that could work. Based on the initial rules, we know that the 4th, 5th, 7th, and 8th floors cannot be cleaned on Wednesday, leaving only 1/2/3/6. On Saturday, the only possibilities are 1/5/6/7. These possibilities are even more constraining when coupled with the rule that consecutively numbered floors are not cleaned on the same day.
To eliminate answer choices, there is some sense in which it is important to try all of them out. However, there are some things that might help expedite this. One is that answer choice (D) "The sixth floor is examined on Thursday" is an answer choice that could be eliminated off the bat. This is because the sixth floor is a random. It's highly unlikely that the random variable's placement would determine all the other ones since the random variable by definition is one without explicit constraints on it.
Left with four answer choices, another way to expedite the process is by only diagramming an answer choice part of the way through without needing to complete an entire diagram for each. This would enable you to test the new condition of each answer choice within the diagram to see if it triggers lots of rules (and thus determines the other variables), or it will lead you in the direction of seeing that no such determination results. For example, answer (A), "Hi mollyquillin!
In diagramming this one out, it seems to me that it's especially important to make sure to include all of the not-laws in the original diagram.
In fact, there were enough not-laws under Wednesday and Saturday that it seemed worthwhile to list the possibilities of variables that could work. Based on the initial rules, we know that the 4th, 5th, 7th, and 8th floors cannot be cleaned on Wednesday, leaving only 1/2/3/6. On Saturday, the only possibilities are 1/5/6/7. These possibilities are even more constraining when coupled with the rule that consecutively numbered floors are not cleaned on the same day.
To eliminate answer choices, there is some sense in which it is important to try all of them out. However, there are some things that might help expedite this. One is that answer choice (D) "The sixth floor is examined on Thursday" is an answer choice that could be eliminated off the bat. This is because the sixth floor is a random. It's highly unlikely that the random variable's placement would determine all the other ones since the random variable by definition is one without explicit constraints on it.
Left with four answer choices, another way to expedite the process is by only diagramming an answer choice part of the way through without needing to complete an entire diagram for each. This would enable you to test the new condition of each answer choice within the diagram to see if it triggers lots of rules (and thus determines the other variables), or it will lead you in the direction of seeing that no such determination results. For example, answer (A), "Hi mollyquillin!
In diagramming this one out, it seems to me that it's especially important to make sure to include all of the not-laws in the original diagram.
In fact, there were enough not-laws under Wednesday and Saturday that it seemed worthwhile to list the possibilities of variables that could work. Based on the initial rules, we know that the 4th, 5th, 7th, and 8th floors cannot be cleaned on Wednesday, leaving only 1/2/3/6. On Saturday, the only possibilities are 1/5/6/7. These possibilities are even more constraining when coupled with the rule that consecutively numbered floors are not cleaned on the same day.
To eliminate answer choices, there is some sense in which it is important to try all of them out. However, there are some things that might help expedite this. One is that answer choice (D) "The sixth floor is examined on Thursday" is an answer choice that could be eliminated off the bat. This is because the sixth floor is a random. It's highly unlikely that the random variable's placement would determine all the other ones since the random variable by definition is one without explicit constraints on it.
Left with four answer choices, another way to expedite the process is by only diagramming an answer choice part of the way through without needing to complete an entire diagram for each. This would enable you to test the new condition of each answer choice within the diagram to see if it triggers lots of rules (and thus determines the other variables), or it will lead you in the direction of seeing that no such determination results. For example, answer (A), "The second floor is examined on Friday" would let you eliminate the possibility of the second floor being washed one Wednesday, leaving a possible 1/3/6 for Wednesday. One would also know that the 8th floor must be on Saturday. Beyond those inferences, however, it's not clear how much else we know.
One would have a similar experience with answer choices (A) through (C). In each case, one would find that plugging in the answer choice would force some variables but not clearly doing so to others; this would be enough reason to eliminate the answer choice, and without having to fill out complete diagrams for those answer choices. One would then see how answer choice (E) uniquely forces the variables into place, especially because of that non-consecutive rule. If it were true that "The eighth floor is examined on Thursday," then we would be left with 1/5/6 as possibilities for Saturday, and could infer that the 1st floor must be there because of the non-consecutive rule. We'd also know that the 2nd floor must before the 8th, so the 2nd must be on Wednesday. The 6th must also be on Wednesday because the 3rd can't go there due to the non-consecutive rule. In short, one can see that (E) forces a chain reaction unlike the others. While you could finish that chain reaction if you like, it would hopefully be obvious before it has fully been diagrammed that it uniquely triggers that chain reaction, even if you don't diagram it out in its entirety.
