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42 votes
Accepted

How many tries to roll a 6?

The answer is indeed...             ...because the question is equivalent to...   Calculations:
  • 21.5k
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 ...
  • 21.5k
37 votes
Accepted

Eccentric Millionaire Probability Paradox

Another way to think about it
  • 16.9k
23 votes
Accepted

Protagoras's Paradox. An Unsolved Court Case

There is no paradox. The teacher should get paid, one way or another. The key to understanding the situation is realizing there are multiple slightly different scenarios that are all being described ...
  • 5,937
20 votes

A library with less information than one of its books

This is indeed possible if we define information content as the least number of bits necessary to describe the data. Consider the following example (in human readable language): Book 1: Jim knows all ...
  • 13.4k
18 votes
Accepted

A library with less information than one of its books

The books in the library contains all binary strings of length 1 million, one per book, sorted in lexicographic order. An individual book takes a million bits to specify, but this description of the ...
  • 24.1k
15 votes
Accepted

Two many rainbows?

Original solution by YowE3K   (who later turned it into this community wiki) This isn't an answer to the exact question, but the following link is to an image that I thought was worth looking ...
15 votes

How many tries to roll a 6?

Let $X_n$ be the event that the dice takes $n$ rolls to get the first 6, given all the rolls are even. Let $A_n$ be the event that it takes $n$ rolls to get the first 6, and let $B$ be the event that ...
  • 21.9k
14 votes

Where did the extra dime come from?

It seems rather obvious to me. Am I missing something? Edit to add this: I see now where there could be an incorrect way to reason about it that some people (like the cashier maybe) might do. It ...
11 votes
Accepted

Birthdays celebrated in wrong order

The twins were travelling eastwards across the International Date Line during their birth. The elder twin brother was born first, on March 1st. After they crossed the International Date Line, the ...
  • 12.5k
11 votes

Eccentric Millionaire Probability Paradox

It is rational for both parties to press the button, causing them to win $500$ on average. Here is what is wrong with the reasoning in the Paradox section. Once Alice is called in, she reasons that ...
  • 31.7k
11 votes

Protagoras's Paradox. An Unsolved Court Case

Case 1. Case 2. Bonus: [EDIT] To answer the question about who's right and wrong...
  • 17.8k
10 votes

Who's the oldest?

I think
  • 9,582
10 votes
Accepted

It's All Paradox - Or Is It?

So indeed it is
9 votes

A library with less information than one of its books

Sorry if this is not in proper mathematical terms, I am not a mathematician...
  • 17.9k
9 votes
Accepted

Who's the oldest?

Legally,
9 votes

How many tries to roll a 6?

I believe the answer is This is computational calculation, so it is not statistical answer. It is for the people who try to find it probabilistically. Here is the probabilistic solution: First of ...
  • 29.2k
8 votes

Birthdays celebrated in wrong order

There's room even for one more day of difference, that is, the elder brother can celebrate his birthday 3 days after the younger brother does. leoll2 says in his answer that they travel across the ...
  • 336
8 votes

Two many rainbows?

I can't see images now, but from the optics laws ang geometry it follows that the center point of the rainbow's arc is opposite to the light source with respect to your eye. In other words, if the ...
  • 1,674
8 votes
Accepted

The faster you walk

This could work: Alternatively (with the same reasoning):
  • 12.6k
7 votes
Accepted

At least $N$ false statements

(1) No statement $n$ with $2\le n\le N$ in the second part can be true, as it would imply its own falseness. Every statement in the second part of the list is false. (2) As statement $n$ with $2\...
  • 45k
7 votes

What happened to the missing £10?

You should be deducting the Bellhop's £20 from the £270, not adding it. Edited with more details: The question is deliberately misleading you into thinking there's a paradox, and some money has gone ...
7 votes
Accepted

Where did the extra dime come from?

Explanation:
  • 7,252
7 votes

Where did the extra dime come from?

7 votes

Protagoras's Paradox. An Unsolved Court Case

The student wins the case and then has to pay back the fee. The claim being made is against a future call: "I will pay you one day"--well there's no actual way to prove that the student failed to ...
  • 71
6 votes
Accepted

Obi-Wan vs Grievous

When you multiplied both sides by $(x-1)$, you introduced the new extraneous solution $x=1$ to the equation. Later on when you divided by $(x-4)$, you forgot to case check that $(x-4)$ might equal $0$....
  • 3,618
6 votes

A list of 100 statements

For the second part, "At least $n$ of the statements in this list are false," you have some number $k$ of false statements, and $100-k$ true statements. It should be clear that the $n^{th}$ statement ...
  • 1,937
6 votes
Accepted

Puzzle : O' Barber , Who Art Thou?

No, you are wrong. The barber is stated to shave "those people, and only those people, who do not shave themselves". If we assume the barber is a person, they cannot exist. If they did exist, ...
6 votes

Protagoras's Paradox. An Unsolved Court Case

This doesn't seem to be that difficult.

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