Brooklyn Nine-Nine: 12 Islanders Riddle

“There are twelve men on an island. Eleven weigh exactly the same amount, but one of them is slightly heavier. You must figure out which. The island has no scale but there is a see-saw. The exciting catch: you can only use it three times.”

Step one:
Split the islanders into 3 groups of 4 (Groups A, B. and C)

See-Saw Round 1:
Group A sits on one side, group B on the other.

If the two groups weigh the same, the heavier islander is in Group C
If either group A or group B is heavier, that group contains the heavier islander.

See-Saw Round 2:
Divide the heavier islanders group in half to make two remaining pairs.
Place a pair on each side of the see-saw.

See-Saw Round 3:
Divide the heavier pair in half and re-balance to discover the ‘slightly heaver islander.’

Background

A plot line in Season 2 Episode 18 of Brooklyn Nine-Nine (S02E18) involved Santiago, Diaz, and Terry (Terry likes to be called Terry) trying to solve a riddle originally presented to Holt by his former captain and mentor. The episode ends without revealing the riddle’s solution.

Various methods have been described to solve for the heavier islander, some with lengthy or extensively mathematical descriptions. The above is offered as a short answer, and possibly the quickest method.

• A 3 page Stonybrook math department PDF
• A Medium post by Ben Birch which uses patterns like so:
person:  A B C D E F G H I J K L
round 1: L L L L R R R R — — — -
round 2: L L R R R — — — L R L -
round 3: L R R — — L R — L L — R

These and other methods are interesting and likely hook into further explorations of methodologies suited to even more complex problem solving.

The if/then groupings used at the top are offered as a less wordy description, in case you’re chatting about the 99 and want to answer the riddle succinctly, or verbally, or just stump your friends ;-)

Nine-Nine!