# Tag Info

Accepted

### How many tries to roll a 6?

The answer is indeed...             ...because the question is equivalent to...   Calculations:
• 21.3k

### 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 ...
• 21.3k
Accepted

Another way to think about it
• 16.8k
Accepted

The biggest problem with the prisoner's proof is that his model is incomplete. One piece of that is that it merges two key variables - days on which the execution can happen, and days on which the ...
• 5,757
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 ...
• 5,757
Accepted

### How can the "Boy or Girl" paradox be worded unambiguously?

I was at a dinner party the other night and I spoke to Mr Smith. He mentioned having two kids, both with unisex names: Sam and Alex. I remember that he told a story about "my son", but I don't recall ...
• 510

### 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 ...
• 13.3k
Accepted

### A boy and his father

The classic answer is "The surgeon is his mother". Another possible answers: It is another father of him. Gays are real.:) It is step-father. No one would care to chose precise words in such ...
• 15.8k
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 ...
• 23.6k
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 ...

### 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 ...
• 21.7k

### 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 ...
• 43.1k

### Mirror Room Puzzle (Thought Experiment)

Basically the mirror line is a physical equivalent of an ideal wall, which can react to any force you apply to it with the same, but opposite force. A physical object can not cross a wall, especially ...
• 15.8k
Accepted

The negation of "All x are y" is "There is at least one x which is not y". So, Epimenides is a liar. Therefore his statement "All Cretans are liars" is false. This means that not all Cretans are ...
• 4,975
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 ...
• 12.4k

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 ...
• 31.3k

### Protagoras's Paradox. An Unsolved Court Case

Case 1. Case 2. Bonus: [EDIT] To answer the question about who's right and wrong...
• 17.7k

I think
• 9,542
Accepted

### It's All Paradox - Or Is It?

So indeed it is
• 114k

The simple (and I believe the only) answer to both your questions is "This is a paradox, so logic does not have predictability power here". Martin Gardner described this paradox in detail. ...
• 15.8k

### A library with less information than one of its books

Sorry if this is not in proper mathematical terms, I am not a mathematician...
• 17.7k
Accepted

Legally,
• 8,548

### 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 ...
• 28.8k
Accepted

There is no paradox as long as you realize that, when you say "all adjectives can be categorized as autological or heterological", the "or" is not exclusive. To explain this a little bit better, let'...
• 5,757

### 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

### 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
Accepted

### The faster you walk

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