# The Impossible Bet

A riddle.

Imagine 100 people at a house, with 3 rooms. They are all betting $100 each. Each box has a unique piece of paper with a number ranging from 1-100. Every one is assigned a random number. If all 100 people find their corresponding number (e.g Person 52 finds Box 52), all get their dollars back. You can search 50 boxes only and you cannot report your findings to your teammates, by shouting, or marking them. If at least one person fails, everyone will fail and the dealer keeps all the dollars. I know this is supposed to be a problem but the answers to this question needs to come in a set of paragraphs. Note by Marvin Mediavillo 1 year, 2 months ago 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. numbered2. 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 1paragraph 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 $2 \times 3$ 2^{34} $2^{34}$ a_{i-1} $a_{i-1}$ \frac{2}{3} $\frac{2}{3}$ \sqrt{2} $\sqrt{2}$ \sum_{i=1}^3 $\sum_{i=1}^3$ \sin \theta $\sin \theta$ \boxed{123} $\boxed{123}$ ## Comments Sort by: Top Newest I think it is related to This TED Video - 12 months ago Log in to reply I think this has been asked before in Brilliant. Here's a reference to the best strategy. You can win about 31% of the time. - 1 year, 1 month ago Log in to reply Nice problem... too bad the OP left out so many crucial details. :-| - 1 year, 1 month ago Log in to reply Okay, Before we start we need to do something I learned elementary school. Let’s Break down the question: Imagine 100 people at a house - There are 100 people participating in the bet with 3 rooms. - This is useless information They are all betting$100 each. - So, we now how much they are betting and how much the host can gain

Each box has a unique piece of paper with a number ranging from 1-100. - 100 participants...

Every one is assigned a random number. If all 100 people find their corresponding number (e.g Person 52 finds Box 52), all get their dollars back. - So, if everyone matches their box everyone gets their money back.

You can search 50 boxes only and you cannot report your findings to your teammates, by shouting, or marking them. - You can search half the boxes - No communication (i.e. not telling your friend that your box is in the corner)

If at least one person fails, everyone will fail and the dealer keeps all the dollars. - 1 person fails, host wins.

Let’s break it down. This is just probability. What is the chance everyone gets their money back? Let’s say I am person 38. I can see 50 of the 100 boxes in order to attempt to get my box. So, I have a 1/2 chance of finding my box. There are 100 people that have a 1/2 chance of winning. So, the probaility goes to 1/200. An equivalent to 0.5%.

So, long story short the host is probably going to earn \$10,000 that night. But, if you are a player, good luck, you will need it.

- 1 year, 1 month ago

I think you want $(1/2)^{100},$ a much smaller probability.

- 1 year, 1 month ago

the answer to WHICH question?

What's the purpose of there being three rooms at the house?

Also, about the people being assigned a "random" number... Can the assigned numbers overlap? -.-

- 1 year, 1 month ago