Search found 118 matches

by mward
Thu Jan 05, 2017 9:03 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71045

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...
by mward
Wed Jan 04, 2017 1:03 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71045

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...
by mward
Sun Jan 01, 2017 1:06 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71045

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...
by mward
Thu Dec 29, 2016 3:08 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71045

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 ...
by mward
Thu Dec 22, 2016 5:50 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71045

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...
by mward
Thu Dec 22, 2016 3:12 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71045

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...
by mward
Thu Dec 22, 2016 10:55 am UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71045

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, ...
by mward
Tue Dec 20, 2016 11:56 am UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71045

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 ...
by mward
Mon Dec 19, 2016 6:44 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71045

Re: Infinite Balls and Jugs [solution]

ucim wrote:Do you perhaps mean "We can split this supertask into ℵ0 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.
by mward
Mon Dec 19, 2016 12:23 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71045

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...
by mward
Sat Dec 10, 2016 11:52 am UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71045

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: ...
by mward
Fri Nov 11, 2016 7:35 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71045

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 ...
by mward
Sat Oct 29, 2016 12:08 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71045

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 ...
by mward
Tue Oct 18, 2016 3:49 pm UTC
Forum: Logic Puzzles
Topic: Infinite Balls and Jugs [solution]
Replies: 611
Views: 71045

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...
by mward
Tue Jul 19, 2016 2:59 pm UTC
Forum: Logic Puzzles
Topic: Monty Hall-ish Problem
Replies: 4
Views: 2594

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...
by mward
Mon Jun 27, 2016 9:19 am UTC
Forum: Logic Puzzles
Topic: Two puzzles for the price of 1!
Replies: 17
Views: 4395

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...
by mward
Fri Jun 24, 2016 12:36 pm UTC
Forum: Logic Puzzles
Topic: Two puzzles for the price of 1!
Replies: 17
Views: 4395

Re: Two puzzles for the price of 1!

Second puzzle (based on a solution I first heard in the mid 1970's):
Spoiler:
Float about rubbing your hands until they are sore. Use the saw to cut the float in half. Two halves make a whole, so jump through the hole to escape the box. Shout for help until you are hoarse. Jump on the horse and ride away!
by mward
Sat May 14, 2016 8:39 am UTC
Forum: Logic Puzzles
Topic: What is the last number (alphabetically)?
Replies: 12
Views: 3952

Re: What is the last number (alphabetically)?

ThemePark wrote:
jaap wrote:
Spoiler:
zero

Even better:
Spoiler:
zilch

Still better:
Spoiler:
zip
by mward
Tue Mar 01, 2016 6:31 pm UTC
Forum: Logic Puzzles
Topic: Two gold nugget puzzle
Replies: 17
Views: 3778

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.
by mward
Mon Feb 08, 2016 5:52 pm UTC
Forum: Logic Puzzles
Topic: Russian Roulette with multiple cartridges
Replies: 4
Views: 2513

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...
by mward
Mon Jan 04, 2016 1:15 pm UTC
Forum: Logic Puzzles
Topic: Escape the bear in the circle?
Replies: 22
Views: 4471

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...
by mward
Wed Dec 16, 2015 11:41 am UTC
Forum: Logic Puzzles
Topic: Factorally growing data storage
Replies: 3
Views: 2227

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 ...
by mward
Mon Nov 23, 2015 1:17 pm UTC
Forum: Logic Puzzles
Topic: Escape the Frictionless Circle
Replies: 136
Views: 26581

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.
by mward
Wed Nov 18, 2015 1:03 pm UTC
Forum: Logic Puzzles
Topic: Escape the Frictionless Circle
Replies: 136
Views: 26581

Re: Escape the Frictionless Circle

Spoiler:
Stretch the tether (without breaking it, of course) to a suitable length. Push the cube away from you. Wait until you reach the edge of the circle.
Or even simpler:
Spoiler:
Untie the rope (without breaking it, of course). Push the cube away from you.
by mward
Mon Oct 12, 2015 9:04 pm UTC
Forum: Logic Puzzles
Topic: E2
Replies: 1
Views: 1060

Re: E2

Spoiler:
the renaissance is an epoch in the culture and spiritual development in western and middle europe cocurrently with religion reformation and follows the antics especially the plato.
by mward
Sat Oct 10, 2015 4:42 pm UTC
Forum: Logic Puzzles
Topic: Timed Bridge Problem
Replies: 5
Views: 3058

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...
by mward
Fri Oct 02, 2015 3:27 pm UTC
Forum: Logic Puzzles
Topic: How many rooms are there in the tower?
Replies: 26
Views: 4510

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...
by mward
Thu Oct 01, 2015 6:45 pm UTC
Forum: Logic Puzzles
Topic: Simplified
Replies: 5
Views: 1951

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: &...
by mward
Thu Oct 01, 2015 6:11 pm UTC
Forum: Logic Puzzles
Topic: Anti-Gambler's Fallacy
Replies: 162
Views: 19219

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...
by mward
Thu Oct 01, 2015 4:47 pm UTC
Forum: Logic Puzzles
Topic: Anti-Gambler's Fallacy
Replies: 162
Views: 19219

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...
by mward
Fri Sep 18, 2015 5:30 pm UTC
Forum: Logic Puzzles
Topic: Anti-Gambler's Fallacy
Replies: 162
Views: 19219

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...
by mward
Fri Sep 18, 2015 4:23 pm UTC
Forum: Logic Puzzles
Topic: Anti-Gambler's Fallacy
Replies: 162
Views: 19219

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...
by mward
Thu Jan 15, 2015 8:33 pm UTC
Forum: Logic Puzzles
Topic: Two guards, two doors, no instructions
Replies: 63
Views: 13910

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...
by mward
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: 386916

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...
by mward
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: 386916

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. ...
by mward
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: 386916

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!
by mward
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: 386916

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...
by mward
Sat Nov 15, 2014 1:05 pm UTC
Forum: Logic Puzzles
Topic: My write-up of the "Blue Eyes" solution (SPOILER A
Replies: 1368
Views: 386916

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".
by mward
Sat Nov 15, 2014 12:58 pm UTC
Forum: Logic Puzzles
Topic: Two guards, two doors, no instructions
Replies: 63
Views: 13910

Re: Two guards, two doors, no instructions

The two guards say in unison: "I always tell the truth. He always lies. That door (each one points to a different door) leads to death, the other leads to freedom. If you ask me one question and ask him none, I will answer it truthfully." This also avoids giving any hint towards the boole...
by mward
Wed Oct 29, 2014 10:58 am UTC
Forum: Logic Puzzles
Topic: Two guards, two doors, no instructions
Replies: 63
Views: 13910

Re: Two guards, two doors, no instructions

This almost works, if a command does not count as a true/false statement: Both guards say the following "I always tell the truth. The other guard always lies. Ask one of us a yes/no question! Choose a door! Choose wisely!" Problem: It doesn't explicitly provide the information that one...

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