In previous editions of Puzzles in Pop Culture, we’ve explored opinions about crosswords, embarked on scavenger hunts with sitcom characters, and even saved New York with brain teasers alongside John McClane in Die Hard with a Vengeance. But it’s rare when a movie or TV show poses a puzzler and leaves it to the audience to solve it.
In “Captain Peralta,” a recent episode of the Fox police sitcom Brooklyn Nine-Nine, a subplot featured Captain Holt posing a brain teaser to his fellow officers.
There are 12 men on an island. 11 weigh exactly the same amount, but one of them is slightly lighter or heavier. You must figure out which.
The island has no scales, but there is a seesaw. You can only use it three times.
With Beyonce tickets going to the person who solved the puzzle, the competition was fierce. Rosa suggested using the seesaw to threaten the men into confessing. Amy and Terry suggested that the first seesaw ride involve putting six men on one side and six on the other, which Captain Holt quickly said wouldn’t work.
As it turns out, Holt was hoping one of his officers would solve the puzzle for him, since he’s been unable to crack it for years. The episode ended without providing the audience with a solution.
Thankfully, your friends here at PuzzleNation Blog would never leave you high and dry like that. Let’s get puzzling!
Now, this WOULD be a simple logic problem if you knew you were looking for someone lighter or you knew you were looking for someone heavier. In that case, a 3×3 ride, 4×4 ride, or even the 6×6 ride Amy and Terry suggested, would eliminate part of the field immediately, and the remaining two uses could determine the heavy person or the light person.
Unfortunately, in Captain Holt’s puzzle, you don’t know if the person is heavier or lighter, which makes this more difficult. For instance, if you knew you were looking for someone heavier, you could immediately eliminate anyone on the side of the seesaw higher in the air. But if you don’t know if the subject in question is lighter or heavier, then you could have a heavier person on one side or a lighter person on the other.
Diabolical.
But, with some careful deduction, you CAN solve this puzzle.
First, let’s identify our 12 castaways with the letters A through L. Now let’s divide them into three groups of four: ABCD, EFGH, and IJKL.
For the first seesaw ride, let’s weigh ABCD vs. EFGH.
There are three possible outcomes:
- They balance, meaning we can eliminate all eight of them and our mystery person is in IJKL.
- ABCD sinks while EFGH rises, meaning there’s a heavier person in ABCD or a lighter person in EFGH, so we can eliminate IJKL.
- EFGH sinks while ABCD rises, meaning there’s a heavier person in EFGH or a lighter person in ABCD, so we can eliminate IJKL.
OUTCOME 1: They balance
For the second seesaw ride, we’ll take IJK and weigh them against any three of the eliminated people — let’s say ABC — because we know they weigh the same.
OUTCOME 1-1: if IJK balances against ABC, we know that L is our guy. For the third seesaw ride, weigh L against A to determine if L is lighter or heavier.
OUTCOME 1-2: if IJK sinks, one of them is heavier than ABC. For the third seesaw ride, weigh I against J. If they balance, K is the heavy one. If I or J sinks, he’s the heavy one.
OUTCOME 1-3: if IJK rises, one of them is lighter than ABC. For the third seesaw ride, weigh I against J. If they balance, K is the light one. If I or J rises, he’s the light one.
OUTCOME 2: ABCD sinks while EFGH rises
For the second seesaw ride, we have eight possible suspects — four heavy, four light — so we mix up the two previous groupings in order to eliminate some suspects. We’ll take E, F, and A and weigh them against G, B, and L. That’s two from the lighter side and one from the heavier vs. one from the lighter, one from the heavier, and one we know is standard.
Again, there will be three possible outcomes:
OUTCOME 2-1: If EFA balances with GBL, they’re all eliminated, leaving either H as a lighter person or either C or D as a heavier person. For the third seesaw ride, weigh C against D. If they balance, H is lighter. If they don’t, whichever is heavier is our guy.
OUTCOME 2-2: If EFA sinks, either A is heavy (because E and F were on the lighter side before) or G is light (because B was on the heavier side and L has already been eliminated), and we can eliminate C, D, and H. For the third seesaw ride, weigh G against L. If they balance, A is heavy. If they don’t, then G is light.
OUTCOME 2-3: If EFA rises, either B is heavy (because G was on the lighter side and L has already been eliminated) or either E or F is light (because A was on the heavier side), and we can eliminate C, D, and H. For the third seesaw ride, weigh E against F. If they balance, then B is heavy. If they don’t, whichever is lighter is our guy.
OUTCOME 3: EFGH sinks while ABCD rises
For the second seesaw ride, we have eight possible suspects — four heavy, four light — so we mix up the two previous groupings in order to eliminate some suspects. We’ll take A, B, and E and weigh them against C, F, and L. That’s two from the lighter side and one from the heavier vs. one from the lighter, one from the heavier, and one we know is standard.
Again, there will be three possible outcomes:
OUTCOME 3-1: If ABE balances with CFL, they’re all eliminated, leaving either D as a lighter person or either G or H as a heavier person. For the third seesaw ride, weigh G against H. If they balance, D is lighter. If they don’t, whichever is heavier is our guy.
OUTCOME 3-2: If ABE sinks, either E is heavy (because A and B were on the lighter side) or C is light (because F was on the heavier side and L has already been eliminated), and we can eliminate D, G, and H. For the third seesaw ride, weigh C against L. If they balance, E is heavy. If they don’t, then C is light.
OUTCOME 3-3: If ABE rises, either F is heavy (because B was on the lighter side and L has already been eliminated) or either A or B is light (because E was on the heavier side), and we can eliminate D, G, and H. For the third seesaw ride, weigh A against B. If they balance, then F is heavy. If they don’t, whichever is lighter is our guy.
This was one whopper of a brain teaser, to be sure, and I’m not surprised it stumped even the likes of the impressive Captain Holt. But, as a special treat, if you’d like to see the Captain himself explain the solution, go here and check out the embedded video. Enjoy.
Of course, it doesn’t answer the real question: who cares about weight? Why aren’t they building a boat to escape the island?
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