Logic Puzzles, vol.2, no.174, Hamlet Understudies

[RaRA]

Is anyone aware of a mistake in clue number three in this puzzle? It clearly says that Ernest performed his usual role on Wednesday. To me that is a positive clue and call number five reads Shane‘s performance was one day after Ernest. Unless I am missing something like rational, thought that means Ernest is on Wednesday and Shane is on Thursday. I went on to complete. The rest of the puzzle only to learn from the answer key that Ernest is on Thursday and Shane is on Friday. Can anyone provide clarification?

[zenobia43]

I will have access to my Vol. 2 this weekend, and if nobody else has responded by then, I'll take a look.

[LLapp]

RaRA, I don't have the book, but I wonder if the key phrase in clue number 3 is "usual role." If the performance days you're tracking are the days when the understudies performed in the role of Hamlet rather than in their usual roles, then the clue means that Ernest did not perform as Hamlet on Wednesday.

[hadrian]

Yeah precisely what LLapp said. If someone is understudying Hamlet, then by definition their usual role is not Hamlet.

[zenobia43]

I just got a look at Vol. 2 174, and LLapp and Hadrian have explained it. Clue 3: "Ernest performed his usual role as expected on Wednesday." is a negative clue rather than a positive clue.

Each of the main actors needed an understudy on one of the days, and this clue is telling you that Ernest's need for an understudy wasn't on Wednesday.

[RaRA]

Thanks again for all your help. Question-clues that are “Of x and y, one was A and the other was B” is decifered the same as “Between X and Y , one was A and the other was B”. Correct?

[zenobia43]

Yes. That is correct.

[LLapp]

RaRA, in case this is useful, here is how I process clues that read “Of X and Y, one was A and the other was B”:

• X does not equal Y.
• A does not equal B.
• X is either A or B.
• X is either B or A.
• Y is either A or B.
• Y is either B or A.
• A is either X or Y.
• A is either Y or X.
• B is either X or Y.
• B is either Y or X.

So that's 10 clues all in one clue.

[RaRA]

Thank you all for your help. It's been a long time since I studied Math, but these clues “Of X and Y, one was A and the other was B”: Should set up to If..., Then.... equations. If X =A, Then Y =B, If X=B, Then Y=A. What confuses me is when there are multiple clues like this. For example, puzzle 196, Vol. 1, Tempting Temp Work. After reading all the clues, my only positive relationship is 50wpm=2wks. My grid shows Valentina = 56wpm or Travel Etc.
3 wks.=Travel Etc. or 56wpm. Clue #2- If 68wpm=Devon, Then Coffeteria=3mos. or if 68wpm=3mos, then Coffeteria=Devon. Clue #6, If Jackson=68wpm, then Binder World=1 mo., if Jackson=1mo, then Binder World=68wpm. The only conclusion I can draw is that 68wpm=Devon or Jackson. Oh boy, my mind is twisted.

[RaRA]

Here is a picture of my grid. The small circles are the possible matches.

[zenobia43]

The "Of X and Y, one is A, and the other is B" clues are very rich sources of negative relations.

As LLapp pointed out, there is a method for checking all the ways of getting those relations.

The one method that is normally missed is the following:

The left side of the clue mentions X. X can either be A or B. You need to check whether B is restricted to a subset of the A choices and thereby restrict X to only those A choices plus the A choice in the clue.

For example, the first half of Clue 6 mentions Jackson and Binder World.

Terminology: Let's call Applicants category X and Businesses category Y. Let's call Typing Speed category A and Employment category B.

Let's call Jackson and Binder World X4 and Y1 to reflect their category and their position in the list of choices.

Similarly, the second half of Clue 6 mentions 68 wpm and 1 month. Let's call those choices A4 and B3.

So, X4 can be A4 or B3. We know that B3 cannot be 50 wpm (A1) because of Clue 5, so B3 can only be A2, A3, and A5. Add A4 from the clue to that list to get the allowable pairings for X4.

X4, then, can only be A2, A3, A4, or A5. Therefore, Jackson cannot be 50 wpm (A1).

We expressed B3 in terms of the A category to find additional restrictions for X4.

I.e. we expressed 1 month in terms of the Typing Speed category to find additional restrictions for Jackson.

Now do the same thing for Y1 (Binder World). The additional restrictions for X4 also hold for Y1 because they're both in the first half of the clue and they will have the same restrictions as the second half.

Once you have finished this exercise for the first half of Clue 6, do the same thing for the second half.

I.e. express Jackson in terms of Businesses and express Binder World in terms of Applicants to find additional restrictions for 68 wpm and 1 month.

This will make your head spin at first, but after a while, you will probably read the clues differently. You might even start to process these "Of X and Y..." clues visually in the grid.

In the more difficult puzzles, you will have to make several passes through these clues.

[RaRA]

OK, so applying the same logic to Clue #2, A4=X2 or x4 OR A4= B4(B4 cannot be A1 or A5, therefore B4 can only be A2, A3 or A4) and Y2=X2 or B4(Which cannot be A1 or A5). Second half of clue, X2=A4 or X2=Y2/B4=A4 or B4=Y2. You're right, my head is spinning. Please check my equations and advise where to go from here.

[zenobia43]

Clue 2 (using the terminology in the earlier post): A4Y2 = X2B4. This is an abbreviated version of your equations.

Let's start the four checks with A4. We want to express X2 in terms of the B category to find additional B category restrictions for A4.

Specifically, for this clue, we want to express Devon in terms of the Employment category to find additional Employment restrictions for 68 wpm.

To do this, check the Devon column to see what restrictions exist for the Employment category. If the only restriction is 3 months, we don't get anything new.

Next, (still working on A4) express B4 in terms of the X category to find additional X category restrictions for A4.

I.e. Express 3 months in terms of the Applicants category to find additional Applicant restrictions for 68 wpm.

To do this, check the 3 months row to see if any additional Applicants restrictions exist. If the only Applicant restriction is Devon, we don't get anything new.

So, now we're done with A4. Since Y2 is on the same side of the equation, we're probably not going to find any new restrictions for that element either.

Let's process X2 next.

Express A4 in terms of the Y category to find additional Y category restrictions for X2.

Specifically, we want to express 68 wpm in terms of the Businesses category to find additional Businesses restrictions for Devon.

Clue 2 has an embedded clue telling us that 68 wpm cannot be Copy Shop. Nice. A4 != Y4 therefore X2 != Y4.

So, that means that Devon cannot be Copy Shop (Y4). Even though 68 wpm cannot be Coffeteria (from the clue), the clue says that Devon could be paired with that Business. We're looking for additional Businesses restrictions for Devon.

Now express Y2 in terms of the A category to find additional A category restrictions for X2.

Specifically, we want to express Coffeteria in terms of the Typing Speed category to find additional Typing Speed restrictions for Devon.

To do this, check the Coffeteria column to see what restrictions exist for the Typing Speed category. If the only restriction is 68 wpm, we don't get anything new.

Finally, let's process B4.

Just like Devon, 3 months cannot be Copy Shop. A4 != Y4 therefore B4 != Y4.

So, after all that checking, all we got was two more Xs in our grid.

Depending on what is in your grid when you do all this processing, you might have gotten more Xs.

After you have processed these "Of X and Y..." clues hundreds of times, your brain will start doing these checks visually in the grid. You won't have to think about the equations.

And I apologize for any errors I may have made in this super lengthy explanation. It's a lot harder to write all this down than it is to read the filtered clue and apply all the mental shortcuts.

[zenobia43]

Also - take a look at the Transitive Relationships (unaligned pair) chapter in the "How to Solve a Logic Puzzle" tutorial. Slide 5 is similar to what I am trying to describe.

https://logic.puzzlebaron.com/how-to-solve-a-logic-puzzle.php?t=transitive-relationships-unaligned-pair

The description in the tutorial leads you in the direction of visual processing rather than using equations.

In particular, look at the green shaded cells in slide 5. Notice the "symmetry?"