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I am trying to improve my logical thinking and I came across this puzzle problem. I need some help solving the puzzle below.

Two weeks ago, four enthusiasts made sightings of objects in the sky in their neighborhood. Each of the four reported his or her sightings on a different day. The FBI came and was able to give each person a different explanation of what he or she had "really" seen. Can you determine the day (Tuesday through Friday) each person sighted the object, as well as the object that it turned out to be?

  • Mr. K made his sighting at some point earlier in the week than the one who saw the balloon, but at some point later in the week than the one who spotted the kite (who isn't Ms. G).
  • Friday's sighting was made by either Ms. Barn or the one who saw a plane (or both).
  • Mr. Nik did not make his sighting on Tuesday.
  • Mr. K isn't the one whose object turned out to be a telephone pole.

I am trying to figure out the logic behind this problem. Can someone help me think logically about the solution?

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  • $\begingroup$ (1) I guess you didn’t create this puzzle.  Even though you aren’t presenting it as your own work, you should probably give credit to the author or original source.  (2) If you do create puzzles like this, a friendly thing to do would be to give all the people names, or use initials for all of them (and not a mixture).  Also it’s common to use A, B, C, and D (e.g., Alex, Bobby, Chris, and Dana).  (3) “Each of the four reported his or her sightings on a different day.” is ambiguous.  If I saw a UFO on Tuesday,  … (Cont’d) $\endgroup$
    – Peregrine Rook
    Commented Dec 11, 2016 at 22:12
  • $\begingroup$ (Cont’d) …  I probably wouldn’t report it (i.e., say something) until after I heard that somebody else had had a similar experience.  If you mean “Each of the four made his or her sightings on a different day.”, say so.  (4) I found the first bullet confusing.  I deleted the second comma, which (IMNSHO) was almost misleading.  I suggest that both occurrences of “at some point” could/should be deleted, as they can be deleted without changing the meaning; as such, they are distracting clutter. $\endgroup$
    – Peregrine Rook
    Commented Dec 11, 2016 at 22:13

1 Answer 1

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Setup

We have four people (B,G,K,N), four objects sighted (balloon, kite, plane, telephone pole), and four days (Tuesday, Wednesday, Thursday, Friday). Here's the information we've been provided with:

  1. K's day was earlier than balloon day.
  2. K's day was later than kite day.
  3. G didn't spot the kite.
  4. Friday was either B's day or plane day (or both).
  5. N's day wasn't Tuesday.
  6. K didn't spot the telephone pole.

Solution

We know K didn't spot the balloon (1) or the kite (2) or the telephone pole (6), so K spotted the plane. Also, K's day can't be Friday (1), so Friday was B's day (4).

We know the kite wasn't spotted by K (2) or G (3). Nor was it spotted by B, since B's day was Friday and the kite can't have been spotted on Friday (2). So N spotted the kite. Also, we know kite day is two days before balloon day (1,2), so kite day must have been Tuesday or Wednesday; but N's day wasn't Tuesday (5), so kite day was Wednesday, which means K's day was Thursday (2) and balloon day was Friday (1).

And the rest we can get by elimination. Summing up:

  • G spotted a telephone pole on Tuesday.
  • N spotted a kite on Wednesday.
  • K spotted a plane on Thursday.
  • B spotted a balloon on Friday.
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    $\begingroup$ @BrandonJ You're very welcome! The key is to examine the information given and see which pieces of it you can put together to make the strongest possible deduction. In this case, the fact that we have three different pieces of information about K suggests we should start by focusing on him, and indeed we can deduce straight away what he spotted, which starts the ball rolling for the next deduction and the next. (By the way, you should have just enough reputation now to upvote this answer as well as accepting it... :-) ) $\endgroup$
    – Rand al'Thor
    Commented Dec 10, 2016 at 17:11

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