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83 votes
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3 doors, three guards, one stone

No questions are required!
StephenTG's user avatar
  • 3,615
63 votes
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100 pieces 1 opportunity, choose wisely!

What you're missing here is the chance of playing at all, given that the game ends when someone finds the prize. (or, chance of finding a prize goes to 0, which is the same thing) ...
Chris Cudmore's user avatar
54 votes
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Deceptive dice game

You can make arbitrarily large sets of dice with this property. Start with Efron's dice: A: 4, 4, 4, 4, 0, 0 B: 3, 3, 3, 3, 3, 3 C: 6, 6, 2, 2, 2, 2 D: 5, 5, 5, 1, 1, 1 A beats B, B beats C, C ...
f'''s user avatar
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52 votes
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Say 100 and win

because:
astralfenix's user avatar
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45 votes
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2 Monkeys on a computer

(a) I claim that the expected typing length are the same for both monkeys. I guess something in my argument will be incorrect, as jafe's answer has 9 approvals, but finding that incorrectness would be ...
Ingix's user avatar
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43 votes
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How many tries to roll a 6?

The answer is indeed...             ...because the question is equivalent to...   Calculations:
humn's user avatar
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43 votes
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Monty Hall Revisited: Winning Both Goats!

Leaving aside the dubious assumption that Monty is entirely on the up-and-up...
Zomulgustar's user avatar
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40 votes

How many tries to roll a 6?

This surprisingly beguiling puzzle may also be solved with a surprisingly unsophisticated approach. Symmetry, by itself, predicts the average length of evens-only sequences ending with 6 to ...
humn's user avatar
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40 votes
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Winning chance in coins game with fixing

GoblinGuide's user avatar
37 votes
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A Bridge Problem

The answer is To see this,
ffao's user avatar
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37 votes

100 pieces 1 opportunity, choose wisely!

Actually,
athin's user avatar
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36 votes
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The "Loop of rope" dilemma

Alice Bob
Gareth McCaughan's user avatar
34 votes
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Simulating an unbiased coin with a biased one

One possibility: This works because: EDIT: Inspired by @trolley813's answer here is a way to recycle the rejected entropy:
loopy walt's user avatar
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33 votes
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How to simulate one die with three dice?

I believe this set of dice satisfies all your requirements:
Deusovi's user avatar
  • 147k
32 votes

2 Monkeys on a computer

(a) Edit: This is incorrect, see comments
Jafe's user avatar
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28 votes

Coin Game with infinite paradox

OK, let's actually take this seriously. As others have said, this is the so-called St Petersburg paradox, and the reason it isn't really much of a paradox is that (1) an extra dollar matters much less ...
Gareth McCaughan's user avatar
28 votes
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Three horse race

A slightly different approach
hexomino's user avatar
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27 votes

Lottery strategy

The average payout for each ticket is So Thus
melfnt's user avatar
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26 votes
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Unfair coins at South Park Elementary v2

As Timmy has a "head" on his shoulders with probability of 1, he always wins at his turn. Then
JonTheMon's user avatar
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26 votes
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Unfair coins at South Park Elementary

Wendy wins on the first flip with probability $1/100$. Otherwise, the game keeps going and Sally has probability $p$ to win on the next flip, which has overall probability $99/100 \times p$. If not, ...
xnor's user avatar
  • 27k
26 votes

2 Monkeys on a computer

Monkey problem To settle down which monkey is faster on average, I'll use Markov chains and Mathematica. Define a state $i$, for $i = 0..6$, as that the monkey 1 has currently written $i$ correct ...
kaba's user avatar
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25 votes
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A Short Dice Puzzle

The answer is Proof Alternative proof
hexomino's user avatar
  • 136k
24 votes

Three horse race

It is The following scenarios are compatible with the information given: Scenario 1: Scenario 2: Scenario 3:
loopy walt's user avatar
  • 21.3k
23 votes

How to simulate one die with three dice?

@Deusovi's answer is totally correct, but I want to add here the general approach for solving such problems as well. No need to upvote, since I did not invent the technique, and you can see it ...
Puzzle Prime's user avatar
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23 votes
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A Short Dice Puzzle II

Answer: Explanation:
AHKieran's user avatar
  • 7,282
23 votes

What is the probability that your life will have lasted for 100 years once you die?

The frequentist answer to this question is This is because
AlmostSure's user avatar
22 votes
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Make 2 dice out of 3 dice

All addition is modulo 6 (e.g. 4 + 3 = 1, 3 + 3 = 6, 5 + 3 = 2, 6 + 1 = 1). 3 Dice Roll Resulting 2 Dice Roll Two same, one different: AAB AB 135 14 246 25 All same: AAA 36 Three in a row: A, A +...
Mike Earnest's user avatar
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22 votes

100 pieces 1 opportunity, choose wisely!

Other people have already given correct answers, but I wanted to suggest a different way of thinking about the question that involves less calculation:
Gareth McCaughan's user avatar
22 votes
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frog on a number line

It's easy to see by transforming the problem into a symmetric one - instead of a 1/3 vs. 2/3 jump to B or D, make a third branch so it's a uniform 1/3 chance of going to B, D, or D' (which in turn has ...
Nuclear Hoagie's user avatar
21 votes
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Socks which may or may not match

The probability of "pairability" is...
Deusovi's user avatar
  • 147k

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