## Search found 121 matches

- Tue Sep 25, 2018 8:00 am UTC
- Forum: Logic Puzzles
- Topic: Where are all the balls?
- Replies:
**15** - Views:
**2793**

### Re: Where are all the balls?

The question reduces to "where is the place that doesn't exist?" Jose Suppose there are ten jugs, labelled 0 to 9, and a ball starts in jug 0. On each step we move the ball from the jug it is in to the next higher jug. After 10 steps, all the jugs are empty: where did the ball go? If we a...

- Mon Aug 13, 2018 10:57 am UTC
- Forum: Logic Puzzles
- Topic: Where are all the balls?
- Replies:
**15** - Views:
**2793**

### Re: Where are all the balls?

In the topic "Infinite Balls and Jugs [solution]" I presented a method for solving supertask puzzles: To calculate the output of any supertask it is sufficient to break down the supertask into a set of finite tasks running in parallel. A "finite task" is a task which completes wi...

- Thu Feb 01, 2018 9:18 am UTC
- Forum: Logic Puzzles
- Topic: Longest Chess Word
- Replies:
**6** - Views:
**3571**

### Re: Longest Chess Word

cabbagehead (11)

https://www.merriam-webster.com/dictionary/cabbagehead

https://www.merriam-webster.com/dictionary/cabbagehead

- Thu Jan 05, 2017 9:03 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**101906**

### Re: Infinite Balls and Jugs [solution]

"Suppose I have infinitely many balls." Even after this one sentence, this hypothetical is already no longer susceptible to observation or experimentation. It thus becomes a question in pure imagination, and as such we can quite reasonably imagine any outcome whatsoever, including the out...

- Wed Jan 04, 2017 1:03 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**101906**

### Re: Infinite Balls and Jugs [solution]

Also, you are generalizing: "The results [of mathematics] apply to the real world" can be interpreted to mean that some mathematical results apply to the real world, which is obviously true and is something I have never denied; or it can be interpreted to mean that all mathematical result...

- Sun Jan 01, 2017 1:06 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**101906**

### Re: Infinite Balls and Jugs [solution]

Instead, we're talking about words that do not string together in such a way as to communicate clearly an observation which we can imagine observing. This places the question on a par with such imponderables as, "What would a horse look like if it were not a horse?" The words each individ...

- Thu Dec 29, 2016 3:08 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**101906**

### Re: Infinite Balls and Jugs [solution]

Why is TCn different from TBn? Well, precisely because it's divided into two halves. In setting up the task you assert the presence of two step numbers- m and n - so if the first halves ever all finish then at that point you will have asserted the presence of step numbers later than all those used ...

- Thu Dec 22, 2016 5:50 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**101906**

### Re: Infinite Balls and Jugs [solution]

If you could answer these 2 questions: 1. What do you think is left at midnight? 2. Could you provide a formal proof for your answer to (1.)? Could you include the set of axioms you use in your proof and following standard rules of inference? 1. an infinite number of balls 2. at each step 10 are ad...

- Thu Dec 22, 2016 3:12 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**101906**

### Re: Infinite Balls and Jugs [solution]

Kryptonaut: please answer the questions in my previous post . In TaskB you perform ω steps removing one ball numbered n at each step, so the set of balls corresponding to N is removed. So, are you agreed that after Task B the jug is empty? Even though, on every finite step the jug contains exactly ℵ...

- Thu Dec 22, 2016 10:55 am UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**101906**

### Re: Infinite Balls and Jugs [solution]

(C) For task C, imagine that the jug is divided into two halves, L and R, and initially all the balls are in the L half. The finite subtasks are TCn: On step int((n-1)/10)+1 move ball n from L to R. On step n take ball n (which will be in side R) out of the jug All other steps: do nothing Firstly, ...

- Tue Dec 20, 2016 11:56 am UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**101906**

### Re: Infinite Balls and Jugs [solution]

I believe what he meant was 'we can split this supertask into a well-ordered set of finite tasks isomorphic to omega, each element denoted TAn for some finite ordinal n', at least that's what I got from it. That is indeed what I mean by "ω finite tasks, TA1, TA2, ...". I acknowledge that ...

- Mon Dec 19, 2016 6:44 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**101906**

### Re: Infinite Balls and Jugs [solution]

ucim wrote:Do you perhaps mean "We can split this supertask into ℵ_{0}finite tasks, TA1, TA2, ... (up to but not including ω) where TAn is the task:"?

The tasks are ordered, so TA1 is the first task, TA2 is the second, and so on.

So the ordinal number is appropriate.

- Mon Dec 19, 2016 12:23 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**101906**

### Re: Infinite Balls and Jugs [solution]

I think that this method can be applied to any supertask: and will either calculate the result, or will prove that the result is indeterminate. I would love to be proved wrong, however, so if you have a counterexample, please post it! :D I like your reasoning, particularly as you seem prepared to a...

- Sat Dec 10, 2016 11:52 am UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**101906**

### Re: Infinite Balls and Jugs [solution]

Below I present a method which I believe solves all the supertask puzzles. First, a resolution of the paradox: The difference is, the count of balls in the jug (9n at every finite step) is not a most basic fact. The presence or absence of any given ball is. This is the key to resolving the paradox: ...

- Fri Nov 11, 2016 7:35 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**101906**

### Re: Infinite Balls and Jugs [solution]

Does there exist a ball (or an infinite collection of balls) numbered 0.9999 recurring? If not, why not? Is it in the jug? If not, at which step was it removed? And if it was removed, what happened to the balls that were added 'after' it was added (since it can't have been the last, as there is no ...

- Sat Oct 29, 2016 12:08 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**101906**

### Re: Infinite Balls and Jugs [solution]

There is no step "ω/10" since there is no (finite or infinite) number which gives ω when multiplied by 10. In case you are not convinced, consider the fact that "ω/10" must be either finite or infinite: (1) If "ω/10" is finite, then ω/10*10 = ω is also finite. But ω is ...

- Tue Oct 18, 2016 3:49 pm UTC
- Forum: Logic Puzzles
- Topic: Infinite Balls and Jugs [solution]
- Replies:
**611** - Views:
**101906**

### Re: Infinite Balls and Jugs [solution]

I have scanned the whole thread, and I don't think that the following explanation has been posted yet: First consider a simplified scenario: Suppose that there are three jugs labelled A, B and C. Initially, jug A contains all the balls (numbered 1, 2, 3, ... and so on). At step n we move the ball la...

- Tue Jul 19, 2016 2:59 pm UTC
- Forum: Logic Puzzles
- Topic: Monty Hall-ish Problem
- Replies:
**4** - Views:
**3116**

### Re: Monty Hall-ish Problem

Assuming that the dealer doesn't want you to win, we can be sure that the dealer will never turn over the single card or any black cards. If the dealer always turns over two red cards when there are at least two red cards in the pile of three, then we have four possibilities which are (roughly) equa...

- Mon Jun 27, 2016 9:19 am UTC
- Forum: Logic Puzzles
- Topic: Two puzzles for the price of 1!
- Replies:
**17** - Views:
**5380**

### Re: Two puzzles for the price of 1!

What dialect do you speak such that sore and saw are homophones? I've never, ever heard that. They don't even have the same vowel for me, let alone the same post-vowel sound (which is "none" for saw). I speak British English, so I don't actually have a dialect :) http://dictionary.cambrid...

- Fri Jun 24, 2016 12:36 pm UTC
- Forum: Logic Puzzles
- Topic: Two puzzles for the price of 1!
- Replies:
**17** - Views:
**5380**

### Re: Two puzzles for the price of 1!

Second puzzle (based on a solution I first heard in the mid 1970's):

**Spoiler:**

- Sat May 14, 2016 8:39 am UTC
- Forum: Logic Puzzles
- Topic: What is the last number (alphabetically)?
- Replies:
**12** - Views:
**4674**

### Re: What is the last number (alphabetically)?

ThemePark wrote:jaap wrote:Spoiler:

Even better:Spoiler:

Still better:

**Spoiler:**

- Tue Mar 01, 2016 6:31 pm UTC
- Forum: Logic Puzzles
- Topic: Two gold nugget puzzle
- Replies:
**17** - Views:
**4773**

### Re: Two gold nugget puzzle

For the theoretical minimum number of weighings, it is possible that no two nuggets weigh the same. In fact it is also possible that no two arbitrary piles of nuggets weigh the same. In this case, any weiging can only give one bit of information. So the minimum number of weighings is at least 7.

- Mon Feb 08, 2016 5:52 pm UTC
- Forum: Logic Puzzles
- Topic: Russian Roulette with multiple cartridges
- Replies:
**4** - Views:
**2870**

### Re: Russian Roulette with multiple cartridges

The solution with no numbers: With random bullet positions: If you spin again, you could get the same chamber again and survive. If don't spin, there is no possibility of getting the same chamber again: all the bullets are still in the smaller number of remaining chambers. So it is better to spi...

- Mon Jan 04, 2016 1:15 pm UTC
- Forum: Logic Puzzles
- Topic: Escape the bear in the circle?
- Replies:
**22** - Views:
**5432**

### Re: Escape the bear in the circle?

It seems the problem the paper is solving only works for an arbitrarily strong bear, but not an infinitely strong bear, as it's being forced to follow some path on a line segment even though it should be able to change directions an infinite number of times in the segment. When using the winning st...

- Wed Dec 16, 2015 11:41 am UTC
- Forum: Logic Puzzles
- Topic: Factorally growing data storage
- Replies:
**3** - Views:
**2494**

### Re: Factorally growing data storage

Why is this in Logic Puzzles? Because it is a logic puzzle! It may not be a very difficult one, but easy puzzles also have their place. For example, if you were giving an "Introduction to Information Theory" course, then this puzzle would make a good exercise. With computer memory, flash ...

- Mon Nov 23, 2015 1:17 pm UTC
- Forum: Logic Puzzles
- Topic: Escape the Frictionless Circle
- Replies:
**156** - Views:
**48840**

### Re: Escape the Frictionless Circle

Push the block away from you in the current direction of the moon: the differential tidal force should create a net acceleration.

- Wed Nov 18, 2015 1:03 pm UTC
- Forum: Logic Puzzles
- Topic: Escape the Frictionless Circle
- Replies:
**156** - Views:
**48840**

### Re: Escape the Frictionless Circle

**Spoiler:**

**Spoiler:**

- Mon Oct 12, 2015 9:04 pm UTC
- Forum: Logic Puzzles
- Topic: E2
- Replies:
**1** - Views:
**1237**

### Re: E2

**Spoiler:**

- Sat Oct 10, 2015 4:42 pm UTC
- Forum: Logic Puzzles
- Topic: Timed Bridge Problem
- Replies:
**5** - Views:
**3397**

### Re: Timed Bridge Problem

it seems counter-intuitive that the fastest person does not carry the torch all the time. It is quite intuitive, when you think about it: The slowest person has to cross at some point (and should not be allowed to cross back). How can you make the most of this time? Have the next slowest pe...

- Fri Oct 02, 2015 3:27 pm UTC
- Forum: Logic Puzzles
- Topic: How many rooms are there in the tower?
- Replies:
**26** - Views:
**5267**

### Re: How many rooms are there in the tower?

The solution assumes incandescent lights, or at least, less then perfectly efficient lights: Turn on the light in the starting room (if it is currently off) and wait a minute or two for it to warm up. Turn it off. Go through and count the rooms one by one until you find a room where the lig...

- Thu Oct 01, 2015 6:45 pm UTC
- Forum: Logic Puzzles
- Topic: Simplified
- Replies:
**5** - Views:
**2204**

### Re: Simplified

5 + 5 = 0 is false, and from a falsehood one can prove anything. Sir Harold Jeffreys in "Scientific Inference" remarks that the fact that everything followed from a single contradiction had been noticed by Aristotle. In a discussion at Trinity High Table McTaggart denied the consequence: &...

- Thu Oct 01, 2015 6:11 pm UTC
- Forum: Logic Puzzles
- Topic: Anti-Gambler's Fallacy
- Replies:
**162** - Views:
**23681**

### Re: Anti-Gambler's Fallacy

Both seem solved because in the abstract logic puzzle case the coin has a 70/30 chance of winning so you should play while in the real world case you should not because the likelyhood of the information in your brain being accurate is less likely than losing 8000 times in a row with a 70/30 coin. I...

- Thu Oct 01, 2015 4:47 pm UTC
- Forum: Logic Puzzles
- Topic: Anti-Gambler's Fallacy
- Replies:
**162** - Views:
**23681**

### Re: Anti-Gambler's Fallacy

b) What if you had to pay $100 for a flip and would get $20 000 if he misses (one time only ;)) (you cannot do any test flips, and he is allways correct) How many times would you flip? 'Son,' the old guy says, 'no matter how far you travel, or how smart you get, always remember this: someday, somew...

- Fri Sep 18, 2015 5:30 pm UTC
- Forum: Logic Puzzles
- Topic: Anti-Gambler's Fallacy
- Replies:
**162** - Views:
**23681**

### Re: Anti-Gambler's Fallacy

A coin can be altered to hit 70-30. A machine tossing with determined result is another question. Every coin toss has a determined result: if you knew the initial conditions of the toss accurately enough, you would be able to predict the result. But you do not know the conditions, so all you know i...

- Fri Sep 18, 2015 4:23 pm UTC
- Forum: Logic Puzzles
- Topic: Anti-Gambler's Fallacy
- Replies:
**162** - Views:
**23681**

### Re: Anti-Gambler's Fallacy

What a fascinating thread. Three pages in and nobody so far has given my answer: (1) I would not play the game at all, because gambling is immoral. (2) "You play 8000 rounds in a row and lose all of them. Do you keep playing?" Clearly this situation cannot arise (see (1)), so let us assume...

- Thu Jan 15, 2015 8:33 pm UTC
- Forum: Logic Puzzles
- Topic: Two guards, two doors, no instructions
- Replies:
**63** - Views:
**15545**

### Re: Two guards, two doors, no instructions

[SETUP] = One of the two doors will not lead to death, one of the two doors will not lead to safety. One of us does not tell the truth, One of us does not tell lies. NOT([SETUP]) = One of the two doors will lead to death, one of the two doors will lead to safety. One of us tells the truth. One of u...

- Tue Dec 30, 2014 9:22 am UTC
- Forum: Logic Puzzles
- Topic: My write-up of the "Blue Eyes" solution (SPOILER A
- Replies:
**1368** - Views:
**405318**

### Re: My write-up of the "Blue Eyes" solution (SPOILER A

A perfect logician needs a reason to accept something as valid. Then we disagree about the definition of "perfect logician". By your definition a "perfect logician" does not believe anything at all. As several people, including myself, have explained: you can only find truth wit...

- Wed Dec 10, 2014 9:24 am UTC
- Forum: Logic Puzzles
- Topic: My write-up of the "Blue Eyes" solution (SPOILER A
- Replies:
**1368** - Views:
**405318**

### Re: My write-up of the "Blue Eyes" solution (SPOILER A

A perfect logician comes to conclusions based solely on valid logic. Assumptions are by definition things you take for granted without questioning their logical validity. Thus a perfect logician cannot assume. In your first sentence your perfect logician takes for granted that logic is valid (i.e. ...

- Sat Nov 22, 2014 10:47 am UTC
- Forum: Logic Puzzles
- Topic: My write-up of the "Blue Eyes" solution (SPOILER A
- Replies:
**1368** - Views:
**405318**

### Re: My write-up of the "Blue Eyes" solution (SPOILER A

Potatoberg wrote:it's the only valid solution that does not require perfect logicians to assume stuff (aka a contradiction).

I would love to see your perfectly logical proof of your assertion that it is a contradiction for a perfect logician to make assumptions. Do not make any assumptions!

- Sun Nov 16, 2014 10:04 am UTC
- Forum: Logic Puzzles
- Topic: My write-up of the "Blue Eyes" solution (SPOILER A
- Replies:
**1368** - Views:
**405318**

### Re: My write-up of the "Blue Eyes" solution (SPOILER A

In the context of the puzzle, a "Guru" is someone whose statements are believed by everyone, and everyone knows that the Guru is a Guru so everyone knows that every knows that... the Guru is believed by everyone". Belief is not logical. These are perfect logicians we are talking abou...