Logic Challenge #15 - The Circus Game

[orion]

Answers are AECCBAD.

Explanations follow.

Clowns: MNOPRSV

Fundamental rule: have 7 to select from, need to select 4 or more

Other rules:
I. must select 2 of RSV
II. !N => O
III. O => R
IV. P => S
V. M => !N

Useful combinations of these rules:
i. II + V: M => O
ii. II + III + V: M => R
iii. II + III: !N => R
iv. I + Fundamental => need 2 or more of MNOP

1. Given: !S
IV: !S => !P
(In other words, "By rule IV, we know that since S is not selected,
neither is P." I hope this format is clear.)
I: !S => RV => answer choices (D) & (E) are false
iv: !P => Need at least two more clowns from MNO.
Possibilities are now NORV, MNRV, MORV, and MNORV.
NORV is a complete set => answer choices (B) & (C) are false.
V: MNRV and MNORV don't work, but MORV does.
Only working possibilities are NORV and MORV => (A) is true.
Answer is (A).

2. Given: Need 5
I: have 2 of RSV => need 3 more from MNOP.
V: MNO and MNP aren't allowed => need MOP or NOP => have OP => (E) is false.
Answer is (E).

3. II: !O => N
V: N => !M
iv: P
IV: P => S => C is true.
Answer is (C).

4. iii: !N => R
iv: !N, !P => MO
I: R => need S or V but not both
Choices are MORS or MORV => (A), (B), (D), & (E) are false, (C) is true.
Answer is (C).

5. I: !R => SV
III: !R => !O
ii: !R => !M
iv: !M, !O => NP
Only possibility is NPSV => (A), (C), (D), & (E) are false, (B) is true.
Answer is (B).

6. Strategy: check each rule one by one and cross off answer choices as they
fail to satisfy a rule.
All choices have 4 or more clowns.
All choices satisfy I.
(D) fails II.
(B) fails III.
(E) fails IV.
(C) fails V.
(A) fails none.
Answer is (A).

7. Strategy: translate all answer choices to lists of clowns selected, then
check each rule one by one and cross off answer choices as they fail to
satisfy a rule.
(A) is NOPSV (fails III)
(B) is MNPSV (fails V)
(C) is OPRSV (fails I)
(D) is MOPRS (fails none)
(E) is NSV (has fewer than four clowns)
Answer is (D).

[orion]

Answers are AECCBAD.

Argh, left out question 8!

8. iii: Either (!N and R) or (N and !R) must be true, so (D) must be false.
Answer is (D).

[rippinradio]

[ianjorgeson]

Hey guys. I liked both sets of explanations. I think you both did a great job of distilling the constraints down and then deriving secondary deductions from them. Rippinradio, I am curious about why you decided to do frames for this game right from the beginning? Did you find that the time you invested early working out each possibility was paid back sufficiently in the time it took to answer the questions? I am personally a fan of frames whenever I can get a game down to 2 basic diagrams. I felt with this game that though the 5 clown diagram was set, once I moved on to considering the 4 clown diagrams, there were enough possibilities that my time was better spent finding those possibilities as I answered individual questions. I'm just curious as to whether you felt spending the time up front finding those possibilities paid off sufficiently in saved time on the questions themselves... Definitely interested in hearing your thoughts, as one thing I sometimes question is whether I am too quick to move to the questions myself.

Thanks for both great explanations.

ps - I felt it was helpful to place conditions I, II, and III directly in my diagram. This meant that from the start, I knew that:

IN ___| OUT
R/S/V | R/S/V
R/S/V | M/N
N/O__|_____

This was helpful to me to really solidify my understanding of precisely how many were in and out, and knowing that one of N/O must be in, just as one of M/N must be out made it easier to quickly eliminate some wrong answers on the later questions.

[rippinradio]

I actually noticed that it could be completed with templates after the fact. You're probably right that the time saved on the questions wouldn't have justified the time spent upfront, but boy were the questions a breeze once the templates were set up.

[tqmorgan]

Hi,

I'm having difficulty understanding the rules, this is how I understand them to be:

I. 2 of R,S,V either RS, RV, SV

if you have RS in then P is in and O is in. You could also add M in which would make it a total of five that are in the group. N would have to be out because it can't be in with O, R or M.

II. If N is not selected then O must be. One or the other must be in but not both.

III. Oscar cannot be selected unless Rascal is selected. O and R must both be selected or not selected at all.

IV. Porky cannot be selected unless Sunny is selected. P and S must both be selected or not selected at all.

V. If M is selected the N can not be. Either M or N is selected but not both.

Combining R2, R3 & R5 would get If N is in then R, O, M can't be.

If V is out then N is out, () then S,P, O, R, M is in, and N can't be in because O, R, M is in and it would violate rules 2 & 5.


For Questions 1.

if S is out, which one of the following must be true?

If S is out, then P is out and R & V are in. Since R is in then O is in then N must be out because it can't be with O, which leaves us with M that must be in to make up a group of four.

Based on the first diagram that is listed it has NORV as being valid, how is this possible?

[ohthatpatrick]

Hey, there.

I can understand why the game is troubling you. It sounds like you're having a lot of trouble dealing with the conditional rules (2 thru 5). It looks like you have an incorrect understanding of all of those.

Have you read the previous posts? Have you studied conditional logic in your strategy guide yet?

Rule 2 looks like this:
~N --> O
~O --> N

This does not mean "one or the other must be in, but not both". It just means "at least one of them must be in". They could both be in.

Consider this scenario:
N and O are selected

Does this break rule 2?
No.
Rule 2 says "if N is NOT selected" ... oh, okay, well then rule 2 doesn't apply, so there's no way this scenario could be breaking it.

Rule 3 looks like this:
O --> R
Rule 4 looks like this:
P --> S

You were acting like it was R --> O and S --> P (because you said RS forces O and P to be selected, which is not true).

If I say, "you can't get your driver's license unless you pass the written test", does that mean
Pass written test --> Get your driver's license ...?

No. You still have to pass the driving test!

What is DOES mean is
Got your driver's license --> Passed written test

"Unless" indicates necessary ideas. Necessary ideas mean "WITHOUT this, you're screwed".

One easy way to translate Unless ideas is to "Un-Left" them. By that I mean you just have to negate the first idea in the sentence.

We translate
"Oscar CANNOT be selected unless Rascal is selected"
into
"If Oscar IS selected, then Rascal is selected"

You also seemed to think of Unless rules as "either they both happen, or they both don't happen".

That is a trap of how we use Unless a lot in real life. If your mom told you, "you can't have dessert unless you eat your veggies", you would naturally think either "you'll eat veggies and get dessert" or "you won't eat veggies and won't get dessert".

But that's not logically valid.

Again, we translate
"you can't have dessert unless you eat your veggies"
into
"If you have dessert, then you ate your veggies"
or
"If you don't eat your veggies, then you can't have dessert"

But it's still possible from this rule that a kid could eat his veggies and STILL not be allowed dessert.

After all, maybe there's another rule that says, "you can't have dessert if you don't clean your room".

A mother might stack tons of necessary requirements on dessert. The kid has to eat veggies, clean his room, and walk the dog.

NOT doing any one of these things is enough to KILL the chances of dessert.

But DOING any one of these things does not GUARANTEE dessert.

"unless" can be tricky because of how we often use it in real life to imply "both things happen or both things don't", but logically it does NOT mean that, so get used to actually turning it into an If/Then statement so you don't fall for that trap.

Finally, rule 5 is
M --> ~N
N --> ~M

You are correct that they can't BOTH be selected, but you're incorrect to think that one of them MUST be selected.

Consider this scenario:
Neither M nor N are selected.

Does it break rule 5?
No.
Rule 5 says "If Marny is selected" ... well in our scenario, M is NOT selected, so Rule 5 doesn't apply, hence it can't be broken.

Take another pass through the game with the correct understanding of the rules and then follow up if you still have questions.

Good luck.