What Is the 12 Men on an Island Riddle?
“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 escapes, but there is a see-saw. The exciting catch? You can only use it three times.”
This puzzle is a variation of the classic “odd coin” problem, but with a twist: you don’t know if the odd person is heavier or lighter, and you have only three weighings to solve the mystery.
Why Did This Riddle "12 Men on an Island" Go Viral?
Brooklyn Nine-Nine Fame: The riddle was featured in Season 2, Episode 18, where Captain Holt challenges his team for Beyoncé concert tickets.
Social Media Buzz: The puzzle resurfaced on platforms like Reddit and Twitter, with fans sharing solutions, memes, and their frustration.
Timeless Appeal: Its roots go back to mathematical logic puzzles that have entertained and challenged thinkers for decades
Step-by-Step Solution: How to Solve the Riddle
The key is to use the seesaw in a way that narrows down the possibilities efficiently. Here’s a proven method, simplified for clarity:
Step 1: Divide and Weigh
- Weigh 1: Split the 12 men into three groups of four (A, B, C, D | E, F, G, H | I, J, K, L).
- Weigh Group 1 (A-D) vs Group 2 (E-H).
Possible Outcomes:
- Balanced: The odd man is in Group 3 (I-L).
- Unbalanced: The odd man is in the heavier or lighter group, but you don’t know which yet
Step 2: Narrow Down
If the first weighing was balanced, weigh three from Group 3 (I, J, K) vs three known “normal” men (A, B, C).
- If balanced: L is the odd man.
- If unbalanced: The odd man is among I, J, K, and you know if he’s heavier or lighter.
If the first weighing was unbalanced, rearrange and weigh to isolate the odd one. For example, swap some from the heavier and lighter groups and compare again
Step 3: Final Weighing
Use the third weighing to compare two suspects directly or compare one with a known “normal” man to determine who is different and whether they are heavier or lighter
Table: Example Weighing Steps
| Weighing | Left Side | Right Side | Result | Next Step |
|---|---|---|---|---|
| 1 | A, B, C, D | E, F, G, H | Balanced | Odd one in I, J, K, L |
| 2 | I, J, K | A, B, C | Balanced | L is odd; weigh L vs A |
| 2 | I, J, K | A, B, C | Unbalanced | Odd one is I, J, or K |
| 3 | I vs J | See result | Odd one identified |
Why Is This Riddle So Hard?
- Unknown Variable: You don’t know if the odd man is heavier or lighter.
- Limited Attempts: Only three weighings, so every move counts.
- Combinatorial Explosion: There are 24 possible scenarios (12 men × 2 possibilities: heavier or lighter)
Origins and History
Riddles like this have a long history, dating back to ancient Sumeria and evolving through Greek and modern mathematical traditions. The “odd coin” variant is a staple in logic and interview puzzles, but the Brooklyn Nine-Nine version brought it to pop culture prominence.
FAQ
Question 1: Is there only one solution to the riddle?
Answer: No, there are multiple ways to organize the weighings, but all efficient solutions follow the same logical principles.
Question 2: Why can’t you just weigh each man individually?
Answer: With only three weighings and 12 people, you must compare groups to eliminate possibilities quickly.
Question 3: What if you know whether the odd man is heavier or lighter?
Answer: If you know this, the puzzle becomes much easier; not knowing is what makes it challenging.
Question 4: Can this method be used for more than 12 people?
Answer: The three-weighing solution is unique to 12 people (with the unknown heavier/lighter variable). For more, you’d need more weighings.
Question 5: Where did this riddle become famous?
Answer: It gained widespread attention after appearing in Brooklyn Nine-Nine, but it’s based on classic logic puzzles
Disclaimer:
This explanation of the "12 Men on an Island" riddle is for educational and entertainment purposes only. The puzzle is a variation of a well-known logic problem and does not originate from any specific scientific or real-world scenario.
