Brooklyn-99 Puzzle

Not sure if anyone here watches Brooklyn 99, but there was a puzzle a few episodes ago and I just wasted a bunch of time figuring out a solution, so I’m gonna clog up this blog by posting it here.  Enjoy!

Puzzle: You have 12 islanders, and one of them is a different weight.  You have a seesaw to weight them with (i.e. it will only tell if a batch of islanders is heavier or lighter than another batch) but may only use it three times.  How do you figure out which islander is different?

My Solution, in the form of solving for each individual islander:

HEAVY and LIGHT are interchangeable (i.e. if solving for opposite, simply reverse all instances of ‘HEAVY’ with ‘LIGHT’ and vice versa)

First four are relatively straightforward, can be done by process of elimination

1. Weighings that will establish 1 as HEAVY:
5-6-7-8 vs 9-10-11-12 : SAME
now you know that any ball from 5-12 is identical and that target is 1, 2, 3, or 4
1-2 vs 3-5 : 1-2 is HEAVIER
here you have established that 1 or 2 is a heavy ball or 3 is a light one
1-3 vs 5-6 : 1-3 is HEAVIER
1 = HEAVY

2. Weighings that will establish 2 as HEAVY:
5-6-7-8 vs 9-10-11-12 : SAME
1-2 vs 3-5 : 1-2 is HEAVIER
again, here you have established that 1 or 2 is a heavy ball or 3 is a light one
1-3 vs 5-6 : SAME
remember you have established that 1 or 2 is a heavy ball, and since 1 is not it…
2 = HEAVY

3. Weighings that will establish 3 as LIGHT:
5-6-7-8 vs 9-10-11-12 : SAME
1-2 vs 3-5 : 1-2 is HEAVIER
again, here you have established that 1 or 2 is a heavy ball or 3 is a light one
1-3 vs 5-6 : 1-3 is LIGHTER
3 = LIGHT

4. Weighings that will establish 4 as HEAVY:
5-6-7-8 vs 9-10-11-12 : SAME
1-2 vs 3-5 : SAME
4 vs 5 : 4 is HEAVIER
4 = HEAVY

5. Weighings that will establish 5 as HEAVY:
5-6-7-8 vs 9-10-11-12 : 5-6-7-8 is HEAVIER
here you have established that either 5-6-7-8 is contains a heavy ball, or 9-10-11-12 contains a light one
5-6-9 vs 7-8-11 : 5-6-9 is HEAVIER
here you have established that either 5 or 6 is a heavy ball, or that 11 is a light one
6-11 vs 1-2 : SAME
5 is HEAVY

6. Weighings that will establish 6 as HEAVY:
Note that 6 is same as 5 except for last weighing
5-6-7-8 vs 9-10-11-12 : 5-6-7-8 is HEAVIER
5-6-9 vs 7-8-11 : 5-6-9 is HEAVIER
6-11 vs 1-2 : 6-11 is HEAVIER
6 is HEAVY

7. Weighings that will establish 7 as HEAVY:
5-6-7-8 vs 9-10-11-12 : 5-6-7-8 is HEAVIER
5-6-9 vs 7-8-11 : 5-6-9 is LIGHTER
here you have established that either 9 is a light ball or that 7 or 8 is a heavy one
8-9 vs 1-2 : SAME
7 is HEAVY

8. Weighings that will establish 8 as HEAVY:
Note that 8 is same as 7 except for last weighing
5-6-7-8 vs 9-10-11-12 : 5-6-7-8 is HEAVIER
5-6-9 vs 7-8-11 : 5-6-9 is LIGHTER
8-9 vs 1-2 : 8-9 is HEAVIER
8 is HEAVY

9. Weighings that will establish 9 as LIGHT:
Note that 9 is same as 7 except for last weighing
5-6-7-8 vs 9-10-11-12 : 5-6-7-8 is HEAVIER
5-6-9 vs 7-8-11 : 5-6-9 is LIGHTER
8-9 vs 1-2 : 8-9 is LIGHTER
9 is LIGHT

10. Weighings that will establish 10 as LIGHT:
5-6-7-8 vs 9-10-11-12 : 5-6-7-8 is HEAVIER
5-6-9 vs 7-8-11 : SAME
10 vs 1 : 10 is LIGHTER
10 is LIGHT

11. Weighings that will establish 11 as LIGHT:
Note that 11 is same as 5 except for last weighing
5-6-7-8 vs 9-10-11-12 : 5-6-7-8 is HEAVIER
5-6-9 vs 7-8-11 : 5-6-9 is HEAVIER
6-11 vs 1-2 : 6-11 is LIGHTER
11 is LIGHT

12. Weighings that will establish 12 as LIGHT:
5-6-7-8 vs 9-10-11-12 : 5-6-7-8 is HEAVIER
5-6-9 vs 7-8-11 : SAME
10 vs 1 : SAME
12 is LIGHT

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14 thoughts on “Brooklyn-99 Puzzle

  1. Also I should point out that the first 4 aren’t as simple as first advertised; originally I thought it wasn’t possible to establish whether one of them (#4 in this case) was heavier or lighter, but it actually is.

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      1. I’ve also won a round of shots. Trivia nights can be fun, but there is always a group of ringers that is OBSESSED with winning. Kinda annoying.

        I’m in LA too. It would be cool if they had the puzzle nights here.

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  2. I’m in Los Angeles. We’ve done trivia nights a couple of times; it’s easy to do well because Millenials aren’t very good at trivia because they’ve always had access to Google.

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    1. Well, then you should print out some of the old puzzles on the website and gather your friends at a bar and have drinks and solve these puzzles. It’s way, way better than any stupid ass trivia night.

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  3. Well done. I haven’t gone through all of them, but your approach seems very sound.

    Where do you live, again, RTD? Because you should go to Puzzled Pint, if it’s in your area. If you’re close to one of the locations listed on the site (http://www.puzzledpint.com/) you should grab a few puzzle-minded friends and go. It’s a damn good time.

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    1. Nice work! I saw the show with the puzzle and I thought about solving it, but I had to take a dump and forgot.

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