# Jacket Problem: Why So Sure? [duplicate]

Three girls graduating high school named: Eshal, Stacy, and Bridgette are playing a probabilistic game where they need to wear jackets of two colors: Bear Brown and Milk White. Initially, their eyes are tied with a cloth so they cannot see what jackets they wore. There are two Bear Brown jackets, and three White Milk jackets, each randomly assigned.

The girls were then to aligned into a tilted straight line in order like:

Stacy--------------------
\                  |
\                 |
\                |
Bridgette       |
\      |
\     |
\    |
Eshal


These lines show the vision of the girls, when the cloth on their eyes will remove (something here implies common sense), then the game begins by removing their eye covering. Stacy can see Bridgette and Eshal, Bridgette can see Eshal, and Eshal cannot see either girl. Also: Girls can hear things behind a wall even :>

Stacy was asked what color was her jacket, to which she said she did not knew. Bridgette was asked the same question, and she was also not certain. At the end, Eshal was asked, this question. She being the most genius girl out there in the school, answered correctly what jacket she was wearing.

What jacket was Eshal wearing (Brown Bear or Milk White)? How was she so sure, in implication: what was the reason that confirmed the color of jacket?

• welcome to puzzling exchange ... this seems to be same puzzle as the old classical 3 hats problem also present here as puzzling.stackexchange.com/questions/201 Jun 27, 2023 at 18:55

Eshal's jacket is

Milk White

Information gained with each question:

Stacy:

If Stacy saw 2 brown jackets, she would know hers is white (cause there's only 2 brown jackets available). But because she said that she didn't know, then there's at least 1 white jacket among Bridgette and Eshal

Bridgette:

There's 3 scenarios since at least one jacket has to be white.
Scenario a: Bridgette has white, Eshal has white.
Scenario b: Bridgette has brown, Eshal has white.
Scenario c: Bridgette has white, Eshal has brown.
If we were in scenario c, Bridgette would know hers is white because there's at least 1 white jacket left in the pair. But because she doesn't know, then we're in either scenario a or b.

Eshal:

That leaves Eshal having a white jacket as the only option.

Side Note:

This answer assumes that Bridgette and Stacey are both perfectly logical people like Eshal, but that wasn't stated in the question :)

• Thanks, correct answer! For the slide information: Stacy and Bridgette barely passed probability theory, and Eshal had a mind like you ;) Jun 27, 2023 at 18:22