Hat Colors (Chapter 4 tab 7)

A complicated answer of 1 is given for the below question after using modulo arithmetic. Wouldn't the easiest solution strategy be for all three of them to agree to always say either "Red, "Green" or "Blue"? Someone must be wearing the Blue (etc.) hat which implies that the probability=1.

Alice, Bob, and Charlie are each wearing a hat, and each hat is either red, green, or blue. They can all see each other's hats, but cannot see their own. At the same time, the three people guess their hat color. They win if any of them correctly guesses their hat color. With a perfect strategy, what is the probability they win the game?

#Logic

Note by A 1
4 years ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list
  • bulleted
  • list

1. numbered
2. list
  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai−1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 ∑i=13 \sum_{i=1}^3
\sin \theta sin⁡θ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

They must specify one color only. They can't say more than 1 color...

Pi Han Goh - 4 years ago

Hi, it looks like you're interpreting the problem is that each hat color must occur once. The way the problem is phrased is that there could be red, green, or blue, but it doesn't have to be one of each; if all three are wearing green then a strategy where they all say "blue" would fail.

Also note in the future, if you have a report like this, if you click on the three dots (either on the top of the screen if you're on in the app, or below "hide solution" if you're in a browser) there is an option called "report problem" which is intended for things like this. It'll get to me faster. Thanks!

Jason Dyer Staff - 3 years, 12 months ago

Also, since the picture might add some confusion, I added a note to clarify that it's not necessarily one of each hat.

Jason Dyer Staff - 3 years, 12 months ago
×

Problem Loading...

Note Loading...

Set Loading...