Logic Game Challenge #37: The Theater Festival Game

[wingedfeetxc]

Our latest Logic Game Challenge, The Theater Festival Game, is live. Post your answer explanations (or questions) questions here. Good luck!

[yhcho]

Is there a way to upload a picture here?
I wrote out an explanation but it accompanies a picture of the diagram.

[timmydoeslsat]

I would upload to an image site like photobucket.com.

At that point, make sure you have the URL address of that image.

Then, when you go to post a message, look for the Img button above the big text box where you normally type a message.

It will come up like this when you hit the Img button:



Make sure you paste the image address between those two brackets in the middle of those two tags.

[img]LIKE%20THIS[/img]

[yhcho]

thanks!
here are the pictures

I never knew posting a thread(or reply) could be this embarrassing
excuse my handwriting.

[timmydoeslsat]

I was going to give my take on this one but yhcho crushed it.

I set this one up in the exact same way of using the days of the week as the base with 2 X's in the afternoon slots for Thurs and Fri. The only thing I did different is that I used an advanced linear format within the individual slots rather than using the subscript, but each works perfectly for this game.

10/10 work by yhcho.

[scott.callin66]

This game took me far longer than the standard 7-10 minutes, anyone else have the same problem?

[timmydoeslsat]

Due to this game having 8 questions, you can expect this game to take a little longer than normal.

Was there anything in particular in the setup or the questions that seemed to slow you down?

[scott.callin66]

For some reason it didn't visually set up very well for me. I did the same thing as the other guys and I actually got all of them right, it just took me 15 minutes to do so. Looking back I might not have made all the inferences I could have but most were situational and based on the information in the question.
Logic Games is by far my best section so I'm not too worried about it I was just wondering if other people found it to be a grind and significantly longer than a normal games section.

[noah]

I worked the game a couple of times in preparation for posting it (and kudos to Ian Jorgeson, the author, and Patrick Tyrrell for editing it) and even the second time found it to be a real tough, time-consuming game.

Usually we aim above the usual LSAT-difficulty level with these games, as we figure students would appreciate the work-out.

[redmessengerbag]

Haaa, it took me about 30 minutes (unfortunately distracted by the annoying thing called work) to do this one and I missed the first question, 7/8, hopefully nothing like this shows up on the LSAT, cuz that'll be the entire section

[scott.callin66]

Good to hear other people are in the same boat. I definitely appreciate the extra difficulty, if you can work through a problem like this the real LSAT should feel like cake.

[rwayersiii]

From the opening paragraph we can set up the following diagram:

Directors: G H I J K L
Writers: M M N N O O

D W D W D W D W
Matinee X X ___ ___ ___ ___

Evening ___ ___ ___ ___ ___ ___ ___ ___
TH F SA SU

The days of the week are chosen as the horizontal base of the diagram because of their inherent order. For each slot we need two spaces, one for the director and one for the writer of the play. Thursday and Friday afternoon are X’ed out because there are no matinees on those days. Now that we have our basic diagram we can move onto the rules.

Rule 1 says that the plays written by M must be performed on the same day; M/M . From this rule we can infer the M will not be the writer for either of Thursday’s or Friday’s shows. The M/M block will thus either be on Saturday or Sunday.

Rule 2 states that I must be performed during either Saturday’s or Sunday’s matinee. I ----- Afternoon Matinee. No further inferences can be made here.

Rule 3 can be diagrammed as follows: J __ > K O > L ___. From this rule we can infer that J can never be the director for any of Sunday’s plays, because if we place J on Sunday then there is not enough room for K and L which must come after J. Similarly, neither K nor L can be the directors on Thursday because of a lack of room for J, and L cannot be the director on Friday because of a lack of room for both J and K which must go before L.

Rule 4 states that all N’s > any M

Rule 5 states that G and M cannot be the writer/director combo for a show.

Rule 6 states H and N cannot be the writer/director combo for a show.

Now that the individual rules are noted we can go ahead and see if we can come up with any inferences by combining rules. Now we said that the M/M block has to come on either Saturday or Sunday, so let’s go ahead and draw those out.




D W D W D W D W
Matinee X X I M K O

Evening J/G N G/J N H M L O
TH F SA SU
If the M/M block is on Saturday we can use rule 4 to conclude N will be the writer for both Thursday’s and Friday’s plays, since all N’s must come before any M’s. So, O will be the writer for Sunday’s plays. From rule 3 we can conclude that K must be the director for the Sunday matinee. The reason for this is because K must come with O and this KO pair must be followed by L. So the only possible solution is to put K with O at the Sunday Matinee which will leave L with O for the Sunday evening show. Next we can use rule 2 to conclude that I must be the director at the Saturday matinee since it is the only matinee left. We can use rule 6 to conclude that H must be the director for the Saturday evening show because Thursday’s and Friday’s shows were both written by N, and H and N cannot be together. This leaves G and J, either of which can be placed on either Thursday or Friday. So if the M/M block is on Saturday we now know the two possible solutions to the game.

On the other hand if the M/M block is on Sunday there is not much we can do.

D W D W D W D W
Matinee X X M

Evening Not J M
TH F SA SU
Not K Not L Not L Not G Not J Not K

It would appear that "I" can still be placed on either Saturday or Sunday’s matinee, so Rule 2 is of little use. From Rule 3 we can conclude that J cannot be selected for Saturday evening or for any of Sunday’s shows. J cannot be on Sunday because if J was there would be no room for K and L which must come after J. J cannot be on Saturday evening because then K would have to come on Sunday Afternoon. Thus, we would get a KM pair which is not allowed. We must have KO. For now J appears capable of appearing in any of the remaining spots. We also know that neither K nor L can come on Thursday since there would be no room for J. L also cannot come on Friday for the same reason. Rule 4 can’t help us at the moment. From rule 5, which states that M and G cannot go together, we can conclude that G cannot come on either of Sunday’s shows. This is all we can do here. On to the questions.

1. We have our two diagrams and we know that Sunday either has the M/M block, in which case we know neither of G/J/K can appear. In our other scenario we know KO has to be the afternoon show and LO has to be the evening show.
A is wrong because I has to be in the afternoon matinee.
B is wrong because we know it must be KO and LO.
C matches perfectly with our first diagram.
D is wrong we know N is never on Sunday.
E is wrong we know from rule 5 G cannot go with M.

2. Firstly, because K is on Friday we can conclude that our M/M block is on Sunday, so we are working with our second diagram. We know this because when the M/M block is on Saturday K must be on Sunday, as we have already worked out.
D W D W D W D W
Matinee X X M

Evening J K O M
TH F SA SU
Not K Not L Not L Not G Not J Not K
If K is on Friday we can use rule 3 to conclude that O must come with K on Friday, and J must be on Thursday. We can’t get anything else here, but the inferences we have made already allow us to answer the question:
A: Is wrong because we know M is on Sunday, thus, by invoking rule 5 we know G can’t come on Sunday.
B: Is wrong because we already know J is the director for Thursday.
C: Is wrong, we already know the M/M block is on Sunday.
E: Is wrong because we know J must come on Thursday.
So through process of elimination we are left with D, the correct answer.

3. Once again we find ourselves using the diagram with the M/M block on Sunday, because we already know that when the M/M block is on Saturday we already know that J is on either Thursday or Friday.

D W D W D W D W
Matinee X X J N I M

Evening G/H N/O H/G O/N K O L M
TH F SA SU
Not K Not L Not L Not G Not J Not K
This question is easier if you already made the inference that J cannot be on Saturday evening. We already did that so we can go ahead and put J in the Saturday afternoon slot. Since J is taking up one matinee we know from rule 2 that I will take up the other. Now we can use rule 3 to infer that the KO pair will be placed in the Saturday evening spot since it must be after J but before L. And L will be placed in the only remaining slot after K which is the Sunday evening spot. Rule 6 tells us that H and N cannot go together. We can use this to conclude that the writer for the play J is directing must be N. If it is not N then it must be O, and in this case N would be on Thursday and Friday and H has to come on one of those days, so this conflict is avoided by putting N with J. This leaves us with dual options on both Thursday and Friday; just remember N and H cannot go together.
From this setup we can easily see that A is the correct response.

4. This is simple since we already came up with the solutions to this scenario. Looking at that diagram with the M/M block on Saturday we see that A, B, and E could be true and are thus incorrect. D cannot be true. C must be true and is therefore the correct answer.

5. If G and H are on the same day then we know we are in the scenario with the M/M block on Sunday because with the M/M block on Saturday G and H are on different days.


D W D W D W D W
Matinee X X G/H O/N I M

Evening J N K O H/G N/O L M
TH F SA SU
Now that we know what scenario we are in it is fairly obvious that H/G have to come on Saturday, since the M/M block is on Sunday and we know from rule 5 that G cannot go with M. We know from rule 6 that H and N cannot go together, so wherever H ends up on Saturday it will be paired with O. Since the Saturday matinee is used up and we know I has to be on a matinee we can place I in the Sunday matinee slot. All that is left is to apply rule 3. We know J can never go on Sunday, Saturday has been used up so J must come on Thursday or Friday. If we put it on Friday there is no room for KO to follow, so J must come on Thursday. Subsequently, KO must come on Friday in order to leave room for L which will fill in the last spot on Sunday Evening. One O is already used up and we need another O and an N for Saturday so the last N has to be placed with J on Thursday evening. Now we can go ahead an attack the answer choices.
It should now be clear that A, B, C, and D all must be true, which leaves us with E which is not necessarily true and is thus the correct answer.

6. Thanks to our diagrams this question can quickly be demolished. We know that when the M/M block is on Saturday, J must be on Thursday or Friday, and if the M/M block is on Sunday J has to be elsewhere or there will be no room for K and L. Therefore, D is correct because we know J can never be paired with M.
Furthermore, in order to eliminate incorrect answers in a must be false question all we have to do is show that the answer could be true. We know from our first diagram with the M/M block on Saturday that B could be true and is thus incorrect. We know from the hypothetical in question 3 that C could be true and is thus incorrect. And the following hypothetical shows that A and E are both possible and thus incorrect.



D W D W D W D W
Matinee X X I N L M

Evening J O K O G N H M
TH F SA SU



But in this question it is easier just to find the one that must be false which is D.

7. The easiest way to go about this question is to eliminate the answers which cannot be true. In our initial inference process we already established that J cannot be on Saturday evening because then there is no room for K and L to follow, so A is incorrect. C is incorrect because we know that either the M/M block is on Sunday, in which case G cannot be on Sunday because of the 5th rule, and if the M/M block is on Saturday we know that G is either on Thursday or Friday, not Sunday. D is incorrect because if O is on Sunday then we know the M/M block is on Saturday in which case I must be with M in the Saturday matinee. E is incorrect because if K is on Sunday evening then there is no room for L to follow. Therefore, by process of elimination we are left with B.

8. GO has to be in either the Saturday or the Sunday matinee. If we put GO in the Sunday matinee, then the M/M will have to fall on Saturday, in which case the two N’s will be put on Thursday and Friday since they have to come before both M’s. So the other O will be put in the Sunday evening spot. Unfortunately since one O is already with G, this O in the Sunday evening slot will have to be the O which needs to be with K, and since this OK pair is in the Sunday evening slot there is no room for L to following. To illustrate:

D W D W D W D W
Matinee X X M G O

Evening N N M K O
TH F SA SU

Thus, this GO pair must be placed in the Saturday matinee spot.

D W D W D W D W
Matinee X X G O I M

Evening J N K O L N H M
TH F SA SU


Since GO is on Saturday the only place for the M/M block is on Sunday. Since GO is in the Saturday matinee, I will go with M in the remaining Sunday matinee slot. Now to apply rule 3, we already know J cannot go on neither Sunday nor the Saturday evening slot, so all that remains is Thursday or Friday. But if J is place on Friday, KO will be forced into the Saturday evening spot and L will be forced with M in the Sunday evening slot. As a result H will be forced into the remaining spot which is Thursday, but the problem is that since both O’s are on Saturday and both M’s are on Sunday H is forced to be paired with N which violated rule 6. Therefore, J must come on Thursday. Now if we place KO in the Saturday evening slot we run into the same problem, except this time H will be forced to pair with N on Friday. And KO cannot go on Sunday evening because then there will be no room for L to follow. Hence, KO must be placed on Friday. Now that both O’s have been place and both M’s have been placed, the two N’s fall into place on Thursday and Saturday evening. We know H cannot go with N, so H will be forced into the Sunday evening slot with M. Now we are left with L which is forced into the only remaining spot which is Saturday evening. Therefore, the correct answer is E or that we can identify all 6 writer/director pairs.

[ohthatpatrick]

Wow, we had two very thorough, very excellent submissions for the explanation contest.

Like the second poster, I also did this game by framing the two options for the 2 m's: Saturday vs. Sunday.

Like many frame-friendly games, one frame fills out almost completely, while the other still has plenty of flexibility.

But it was very cool to see how the first poster did the game without these frames -- just a reminder that there's no "correct" way to get through a game.

In the end, since both were very thorough and modeled great thinking skills, it was basically a tie. In this case, tie goes to the original poster and the one with an easier to read diagram, thanks to uploading an image.

Unfortunately, it's really hard to make diagrams look correct in this typing environment, because once you hit "Submit", all the empty spaces are removed. So the second poster's diagram looks out of alignment and is pretty hard to read.

In the future, feel free to use something like Photobucket or just upload your own .pdf / image file of your diagram. Photobucket hosts your image, so you can get it to appear in your forum post via an [img] tag. But if you attach your diagram as a file, that's cool. We'll read it.

Thanks again for participating. Congratulations, Yhcho!

[caitlinfitz10]

Hi, I'm still confused by the last question. Although H must be on Sunday written by M, why does it have to be evening? Couldn't it be the matinee as well? And Can't I and L switch either Saturday or Sunday? Since J and K are on Thursday and Friday and nothing says that I or L have to be written by a particular writer. So we could have:
Thursday ev: Jn,
Friday ev: Ko,
Saturday m: Go,
Saturday ev: Ln,
Sunday m: Im,
Sunday ev: Hm

BUT we could also have:
Thursday ev: Jn,
Friday ev: Ko,
Saturday m: Go,
Saturday ev: In
Sunday m: Hm
Sunday ev: Lm

So we only know for sure the writer, director and time slot for 3 of the slots: Jn on Thursday evening, Ko on Friday evening, and Go on Saturday matinee...

I must be missing something since the answer is 6 slots, but I'm just not seeing what it is? Thanks for any help you can offer!

[mcdonell52]

^ I think you forgot the rule which states that I can only be a matinee, thus leaving the former answer as the only workable one.

That said, this one took forever for me, and I only got 5/8. Guess I have some practicing to do!