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        riddles >> easy >> Infinity
        
(Message started by: alien2 on Jan 26^th, 2023, 3:26am)

Title: Infinity
Post by alien2 on Jan 26^th, 2023, 3:26am

1) How much is half of infinity? And in which country it lives?
2) If God, by giving a command in simulacrum, tears down a googol trees at random in a pine forest with an infinite number of trees, all at equal distances from adjacent trees, and then you’re teleported at random to this forest, of course, in another dimension similar to virtual reality and by creating your digital projection, what are the odds of stumbling right away at minimum one harvested tree?

Title: Re: Infinity
Post by rmsgrey on Jan 26^th, 2023, 9:28am

1) Half of infinity is either still infinity, or something like "infi"

2) You'll have to be more specific about your randomness because you can't do a uniform distribution over an infinite range - you get a divide-by-infinity error.

Title: Re: Infinity
Post by alien2 on Jan 27^th, 2023, 1:33am

1. Right on both counts, more or less. The intended answer is cast in the same mold; perhaps You can infer it, which in addition suggests in which country a part of infinity lives.

2. Perhaps you can assist me with that. How about a pine forest with a googol number of trees, each at equal distance from adjacent trees, and ten trees are torn down at random?

Title: Re: Infinity
Post by rmsgrey on Jan 27^th, 2023, 8:56am

on 01/27/23 at 01:33:46, alien2 wrote:

2. Perhaps you can assist me with that. How about a pine forest with a googol number of trees, each at equal distance from adjacent trees, and ten trees are torn down at random?

That gives you something you can work with. The next question is what counts for "stumbling right away" - the chance of the closest tree being one of the ten picked trees is 10/googol or 10^-99, but the more trees you count as in range for being stumbled upon, the better your chances. Technically, the precise probability will need to account for the possibility of having multiple trees in range which reduces the probability of having any slightly, but you can get an excellent approximation for any reasonable number of trees in range (say fewer than 10^20) by just multiplying 10^-99 by the number of trees in range.

Title: Re: Infinity
Post by alien2 on Jan 27^th, 2023, 2:25pm

on 01/27/23 at 08:56:03, rmsgrey wrote:

(...) but you can get an excellent approximation for any reasonable number of trees in range (say fewer than 10^20) by just multiplying 10^-99 by the number of trees in range.

I think I'll go with that (math is not my strong suit). I reckon You are 100% sure there is no way to randomize the harvested trees when infinity has a role. Oh well.

Title: Re: Infinity
Post by rmsgrey on Jan 28^th, 2023, 6:13am

on 01/27/23 at 14:25:33, alien2 wrote:

I think I'll go with that (math is not my strong suit). I reckon You are 100% sure there is no way to randomize the harvested trees when infinity has a role. Oh well.

There are ways to randomise them, just not ways that give every tree an equal chance of being picked.

The probability distribution has to sum to 1, but for any probability greater than 0, e, no matter how small, there's a finite number of trees, N, where e*N>1. And infinitely many trees will make the total infinite. If the probability for each tree is 0, then the sum of all the probabilities is stuck at 0, and you still don't get a valid distribution.

To achieve a total of 1, you need to have some trees with higher, and some with lower probabilities.

Title: Re: Infinity
Post by alien2 on Jan 29^th, 2023, 8:44am

Any ideas for the 2nd part of the 1st question? The answer is a bit witty to me.

Title: Re: Infinity
Post by rmsgrey on Jan 30^th, 2023, 2:21am

on 01/29/23 at 08:44:25, alien2 wrote:

Any ideas for the 2nd part of the 1st question? The answer is a bit witty to me.

Well, the two letter country code for Finland is FI, so...

Though you may be thinking of Italy's IT.

Title: Re: Infinity
Post by alien2 on Jan 30^th, 2023, 2:49am

Your modesty is excused, it is very human. And since You are extremely close, or too kind to give away the expected answer, which is cast in the same mold, I'll do a terrible thing and convey the answer I had in mind: "Finn". So Finland it is. What say You? Any inconsistencies, illogical dimensions? I've moments of clarity, thus at times I need reassurance.

Title: Re: Infinity
Post by rmsgrey on Jan 31^st, 2023, 8:52am

on 01/30/23 at 02:49:08, alien2 wrote:

I was thinking that half of "infinity" is "in FI".

My minor niggle with your "Finn" solution is that it requires you to not only discard half the letters, but also discard the ordering of the letters - if you keep the relative order, depending on which 'i' you keep, you end up with "infn", "nfin" or "nfni". "In FI" works with the most natural split - "infi"/"nity". Italy comes from a slightly less good "inf"/"init"/"y"

Title: Re: Infinity
Post by alien2 on Jan 31^st, 2023, 9:07am

I like Your idea! It's better than the expected answer.