If Anna flies in plane 4 and Dave flies in plane 2, which one of the following must be true?

Charlotte on August 9, 2019


Can you please explain this game? Is there something missing?


Irina on August 9, 2019

It is a tricky game indeed! Let's look at the setup:

(1) 4 planes 1,2,3,4 are available to fly. Notice the word "available," it means that there is no requirement that all actually do fly.

(2) 3 pilots -ABC, and 3 copilots - DEF are ALL aboard planes.

(3) No plane flies in the show without a qualified pilot.

These two rules tell us that there are at most three planes actually flying in the show because no plane can fly without a pilot.

p ___ ___ ___ ___
c ___ ___ ___ ___
1 2 3 4

(4) A only flies in either #1 & #4
(5) D only flies in either #2 or #3

These rules tell us that there is a minimum of 2 planes flying the show, since someone other than A has to fly the plane that D is on. Combined with the previous rules, we know that we have at least 2 and at most 3 planes participating in the show.

p /A ___ ___ /A
c ___ /D /D ___
1 2 3 4

Let's look at the scenario in question:

If A flies in #4 and D flies in #2, which of the following MUST be true?

p ___ ___ A
c ___ D ___ ___
1 2 3 4

This setup shows us that planes #2 and #4 definitely fly in the show, and at most one other plane - either plane #1 or #3 but not both could fly in the show. Let's look at the answer choices:

(A) C flies in #1 and #3. It could be true that she flies in #1 or #3, but it could also be true that C flies in #2 and B flies in #1 or #3. Since it only could be true, and we are looking for a MUST BE TRUE answer, (A) is wrong;

(B) If C flies in #3, B flies in #2. Let's quickly diagram this:

p ___ C A
c ___ D ___ ___
1 2 3 4

If C is #3 and A is #4, someone has to pilot #2 with copilot D in it, since D cannot fly plane #2 alone. Since we only have 1 pilot left - B, he MUST pilot plane #2, thus this is the correct answer choice. Plane #1 is out of the show since we assigned all 3 pilots.

Let's briefly look at the remaining options:

(C) B and 1 other person fly in plane 1. That again could be true, B could fly plane #1, and C could fly #2. plane #3 is out of the show in this scenario. But B could also fly plane #3 with another person, and plane #1 would be out of the show. Since this answer choice is could be true rather than MUST BE TRUE, it is wrong.

(D) If B is aboard #4, C flies in #3. This is impossible, someone needs to fly #2 and if A & B is aboard #4 and C flies #3, then no pilots are available for plane #2.

(E) If C flies in #2, B flies in #3. It could be true, but it is also possible for C to fly #2 and B fly #1, or B fly #2 and C fly #1 or # 3. Thus, this is only one of many possible options and is not a MUST BE TRUE choice we are looking for.

Does this make sense?

Let me know if you have any further questions.