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Topic: Tower of Brahma (Read 2317 times) |
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Mermaid
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Tower of Brahma
« on: 2004-02-26 10:56:09 » |
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it seems that there are diff versions of this puzzle...i know the answer..but it doesnt matter because i dont know how the answer is derived..know how this is done? anyone?
This, so the legend has it, is a temple in Benaras. They say that when the great lord Brahma created the world he put up three diamond sticks, mounted on a brass plate, beneath the dome that marks the centre of the world. Upon one of the sticks he placed 64 golden discs. The biggest at the bottom, all decreasing in size, to the smallest at the top. The temple priests have the task of transposing the discs from one stick to the other, using the third as an aid. They work day and night, but must transpose only one disc at a time and must not put a bigger disc on top of a smaller one. When their task is complete, the legend says, the world will disappear in a clap of thunder.
How many transpositions does it take for the job to be done?
(end)
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Kid-A
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RE: virus: Tower of Brahma
« Reply #1 on: 2004-02-26 18:47:55 » |
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4095?
i'm sure it's just (n^2)-1 or something like that. Not sure about the clap
of thunder or the disappearing world though.
>From: "Mermaid" <hidden@lucifer.com>
>Reply-To: virus@lucifer.com
>To: virus@lucifer.com
>Subject: virus: Tower of Brahma
>Date: Thu, 26 Feb 2004 08:56:09 -0700
>
>it seems that there are diff versions of this puzzle...i know the
>answer..but it doesnt matter because i dont know how the answer is
>derived..know how this is done? anyone?
>
>This, so the legend has it, is a temple in Benaras. They say that when the
>great lord Brahma created the world he put up three diamond sticks, mounted
>on a brass plate, beneath the dome that marks the centre of the world. Upon
>one of the sticks he placed 64 golden discs. The biggest at the bottom, all
>decreasing in size, to the smallest at the top. The temple priests have the
>task of transposing the discs from one stick to the other, using the third
>as an aid. They work day and night, but must transpose only one disc at a
>time and must not put a bigger disc on top of a smaller one. When their
>task is complete, the legend says, the world will disappear in a clap of
>thunder.
>
>How many transpositions does it take for the job to be done?
>
>(end)
>
>----
>This message was posted by Mermaid to the Virus 2004 board on Church of
>Virus BBS.
><http://virus.lucifer.com/bbs/index.php?board=61;action=display;threadid=29971>
>---
>To unsubscribe from the Virus list go to
><http://www.lucifer.com/cgi-bin/virus-l>
Hmmm.....PUB!
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simul
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Re: virus: Tower of Brahma
« Reply #2 on: 2004-02-26 19:50:58 » |
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It's easy to find the pattern. Just do it manually with a few and extrapolate.
-----Original Message-----
From: "David Andrew" <dave_is_brewing@hotmail.com>
Date: Fri, 27 Feb 2004 02:47:55
To:virus@lucifer.com
Subject: RE: virus: Tower of Brahma
4095?
i'm sure it's just (n^2)-1 or something like that. Not sure about the clap
of thunder or the disappearing world though.
>From: "Mermaid" <hidden@lucifer.com>
>Reply-To: virus@lucifer.com
>To: virus@lucifer.com
>Subject: virus: Tower of Brahma
>Date: Thu, 26 Feb 2004 08:56:09 -0700
>
>it seems that there are diff versions of this puzzle...i know the
>answer..but it doesnt matter because i dont know how the answer is
>derived..know how this is done? anyone?
>
>This, so the legend has it, is a temple in Benaras. They say that when the
>great lord Brahma created the world he put up three diamond sticks, mounted
>on a brass plate, beneath the dome that marks the centre of the world. Upon
>one of the sticks he placed 64 golden discs. The biggest at the bottom, all
>decreasing in size, to the smallest at the top. The temple priests have the
>task of transposing the discs from one stick to the other, using the third
>as an aid. They work day and night, but must transpose only one disc at a
>time and must not put a bigger disc on top of a smaller one. When their
>task is complete, the legend says, the world will disappear in a clap of
>thunder.
>
>How many transpositions does it take for the job to be done?
>
>(end)
>
>----
>This message was posted by Mermaid to the Virus 2004 board on Church of
>Virus BBS.
><http://virus.lucifer.com/bbs/index.php?board=61;action=display;threadid=29971>
>---
>To unsubscribe from the Virus list go to
><http://www.lucifer.com/cgi-bin/virus-l>
Hmmm.....PUB!
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First, read Bruce Sterling's "Distraction", and then read http://electionmethods.org.
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Mermaid
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Re:Tower of Brahma
« Reply #3 on: 2004-02-26 21:24:16 » |
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right...but there ought to be a method to it...we learn pages and pages of formulas in high school...but how do you know where to use what?...
surely, you too were told that mathematics is practical..that it is useful in everyday life...its not just addition and subtraction! its a way of thinking...problem solving? i wish i can say that i remember everything i learnt at school...NOT....its very depressing..its almost as if all that learning isnt useful to me at all...
i got that...2^64-1...but how do you GET to that? (other than extrapolation)
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rhinoceros
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Re:Tower of Brahma
« Reply #4 on: 2004-02-27 00:45:57 » |
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I knew it as "Towers of Hanoi". Nice problem. It is often found in computer programming textbooks, in the chapter about regression, because it is a rare clear case where regressive thought is the intuitive way to go. You know... things like "if I have solved it for n disks, how do I solve it for n+1 disks". Old plain sequential thought is at a disadvantage here.
Hmm... let's see.
Let's say I solved it for 3 disks and it took me n moves to move them, say, from pin A to pin B.
But... oops... I just noticed there was a 4th disk left at A. Now I need to move that 4th disk from A to C (1 move), and then repeat whatever I did at the beginning and move the other 3 disks on top of it, from B to C (n moves again).
So, if I need n moves to solve the problem for k disks, I need 2n+1 moves to solve it for k+1 disks.
So, let's say that for 4 disks we need n4 moves:
n4 = 2*n3+1 = 2*(2*n2+1)+1
= 2*(2*(2*1+1)+1)+1
= 2^3 + 3^2 + 2^1 + 2^0
Damn... we will still need to use a cookbook formula. This last result is a powerseries:
2^(n-1) + 2^(n-2) +...+ 2^1 + 2^0 = 2^n - 1
And the result is 2^n - 1. It is not hard to give a formal proof using mathematical induction, but I think the answer is better understood by using this "construction" method.
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rhinoceros
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Re: virus: Re:Tower of Brahma
« Reply #5 on: 2004-02-27 06:59:40 » |
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[rhinoceros1]
<snip>
I knew it as "Towers of Hanoi". Nice problem. It is often found in
computer programming textbooks, in the chapter about regression, because
it is a rare clear case where regressive thought is the intuitive way to
go. You know... things like "if I have solved it for n disks, how do I
solve it for n+1 disks". Old plain sequential thought is at a
disadvantage here.
<end snip>
[rhinoceros2]
Scratch out "regression" and "regressive", make it "recursion" and
"recursive". Pardon my Chinese.
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Mermaid
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Re:Tower of Brahma
« Reply #6 on: 2004-02-27 11:55:43 » |
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hey! the rhino is still alive...
ok..here is another one..how do you 'arrive' at the solution...
"can you combine eight 8s with any other mathematical symbols except numbers to represent exactly 1000? you may use addition, subtraction, multiplication, division signs."
everyone probably knows the answer to this too...these are one of the more popular puzzles...but how do you train your mind to 'arrive' at the solution...its one thing to keep reading it over and over until you can recite it as a party trick to impress..and totally another when the solution and the way to the solution looks clear...it feels as though i am missing out on a 'way of thinking'...of problem solving...
also...do we really use algebra in our everyday lives? really..do we?
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Lise Carlstrom
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Re: virus: Re:Tower of Brahma
« Reply #7 on: 2004-02-27 13:05:57 » |
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--- Mermaid <hidden@lucifer.com> wrote:
> also...do we really use algebra in our everyday
> lives? really..do we?
Humor writer Erma Bombeck claimed, "In real life,
there is no such thing as algebra."
My mother heartily agreed, until, as the manager of a
restaurant, she needed to be able to figure out the
original bill before tip, when she had the total with
tip. I showed her how, since this is easy with
algebra; I don't know how you'd do it otherwise.
--Eva
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simul
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Re: virus: Re:Tower of Brahma
« Reply #8 on: 2004-02-27 15:09:27 » |
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You break the big problem into lots of little problems.
-----Original Message-----
From: "Mermaid" <hidden@lucifer.com>
Date: Fri, 27 Feb 2004 09:55:43
To:virus@lucifer.com
Subject: virus: Re:Tower of Brahma
hey! the rhino is still alive...
ok..here is another one..how do you 'arrive' at the solution...
"can you combine eight 8s with any other mathematical symbols except numbers to represent exactly 1000? you may use addition, subtraction, multiplication, division signs."
everyone probably knows the answer to this too...these are one of the more popular puzzles...but how do you train your mind to 'arrive' at the solution...its one thing to keep reading it over and over until you can recite it as a party trick to impress..and totally another when the solution and the way to the solution looks clear...it feels as though i am missing out on a 'way of thinking'...of problem solving...
also...do we really use algebra in our everyday lives? really..do we?
----
This message was posted by Mermaid to the Virus 2004 board on Church of Virus BBS.
<http://virus.lucifer.com/bbs/index.php?board=61;action=display;threadid=29971>
---
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First, read Bruce Sterling's "Distraction", and then read http://electionmethods.org.
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DrSebby
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...Oh, you smell of lambs!
    
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Re: virus: Re:Tower of Brahma
« Reply #9 on: 2004-02-27 18:23:39 » |
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...considering that what you described would be "x + xy = 40$" where y
could equal zero, it would be quite impossible to determine what the bill
was if the total posting tip was all you had. tipping percentages range
wildly, remember.
DrSebby.
"Courage...and shuffle the cards".
----Original Message Follows----
From: Eva-Lise Carlstrom <evalise@yahoo.com>
Reply-To: virus@lucifer.com
To: virus@lucifer.com
Subject: Re: virus: Re:Tower of Brahma
Date: Fri, 27 Feb 2004 10:05:57 -0800 (PST)
--- Mermaid <hidden@lucifer.com> wrote:
> also...do we really use algebra in our everyday
> lives? really..do we?
Humor writer Erma Bombeck claimed, "In real life,
there is no such thing as algebra."
My mother heartily agreed, until, as the manager of a
restaurant, she needed to be able to figure out the
original bill before tip, when she had the total with
tip. I showed her how, since this is easy with
algebra; I don't know how you'd do it otherwise.
--Eva
__________________________________
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Lise Carlstrom
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Re: virus: Re:Tower of Brahma
« Reply #10 on: 2004-02-27 19:05:38 » |
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In the situations I was describing, the tip was set at
15%, as was always true for both special events and
tables of 8 or more.
--Eva
--- Dr Sebby <drsebby@hotmail.com> wrote:
> ...considering that what you described would be "x +
> xy = 40$" where y
> could equal zero, it would be quite impossible to
> determine what the bill
> was if the total posting tip was all you had.
> tipping percentages range
> wildly, remember.
>
>
>
> DrSebby.
> "Courage...and shuffle the cards".
>
>
>
>
>
> ----Original Message Follows----
> From: Eva-Lise Carlstrom <evalise@yahoo.com>
> Reply-To: virus@lucifer.com
> To: virus@lucifer.com
> Subject: Re: virus: Re:Tower of Brahma
> Date: Fri, 27 Feb 2004 10:05:57 -0800 (PST)
>
>
> --- Mermaid <hidden@lucifer.com> wrote:
> > also...do we really use algebra in our everyday
> > lives? really..do we?
>
> Humor writer Erma Bombeck claimed, "In real life,
> there is no such thing as algebra."
>
> My mother heartily agreed, until, as the manager of
> a
> restaurant, she needed to be able to figure out the
> original bill before tip, when she had the total
> with
> tip. I showed her how, since this is easy with
> algebra; I don't know how you'd do it otherwise.
>
> --Eva
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rhinoceros
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Re:Tower of Brahma
« Reply #11 on: 2004-02-27 19:50:30 » |
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[Mermaid]
hey! the rhino is still alive...
[rhinoceros]
Yes, he is. But... having to deal with my own shit over here, it took a good bait such as this thread to make me post something 
[Mermaid]
ok..here is another one..how do you 'arrive' at the solution...
"can you combine eight 8s with any other mathematical symbols except numbers to represent exactly 1000? you may use addition, subtraction, multiplication, division signs."
everyone probably knows the answer to this too...these are one of the more popular puzzles...but how do you train your mind to 'arrive' at the solution...its one thing to keep reading it over and over until you can recite it as a party trick to impress..and totally another when the solution and the way to the solution looks clear...it feels as though i am missing out on a 'way of thinking'...of problem solving...
[rhinoceros]
I didn't know the answer to this one. After one hour of fruitless efforts I had to google it (the answer is the deceivingly simple 888+88+8+8 ).
It seems incredibly difficult to find the answer in a straightforward way. You have to try to find a particular combination of arithmetic operations (additions, subtractions, multiplications, divisions) acting not only on (combinations of) 8s but also on 88s (=8*10+8 ) and 888s (=8*10^2+8*10+8 ). A computer program would have to use a heuristic tree search, applying some kind of "forward pruning" to the "not promising" branches (for example, when you examine an addition of numbers ending in 8, as is the case with the solution, you only examine additions of 5 terms so that the result ends in 0).
If I am not missing something from maths, this seems to be a problem where a human would have to "think like a computer" (unlike the towers problem). However, this was also true for many other problems, which seem easy today with the mathematical tools we have developed (like the towers problem).
So, my best answer to the question "How do you find it" is "Make smart guesses, take shortcuts wherever possible (familiarity with number theory helps here), and take your time..." It seems good for practicing your associative reasoning (your intuition, if you prefer.) A computer is quite good at this kind of problems, since there is a huge literature on smart heuristic searches.
[Mermaid]
also...do we really use algebra in our everyday lives? really..do we?
[rhinoceros]
Some never do, some do and find a few uses for it, and some do and find a lot of uses for it. There is also a rumor about some weirdos using calculus in their everyday lives, but I can only confirm that some use probability theory.
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Mermaid
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Re:Tower of Brahma
« Reply #12 on: 2004-02-28 07:05:23 » |
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ok..just because you spent so much time on it..
here goes:
(8+ /8*(8*8*8--8 = 1000
(8888-888)/8=1000
[(88-/0.8] * [8+(8+/8] = 1000
8[(8*+(8*]-8-8-8 = 1000
[8(8+-(8+8+/8]/8 = 1000
the funny thing is that the woman who put together this puzzle book calls herself the 'human computer'...
how will you write a computer program to get the solution for this problem?
problem #3:"Can you name the smallest number, which when divided by 10 gives a reminder of 9, when divided by 9 gives 8 as the reminder, when divided by 8 gives 7 as the remainder and so on, down to a remainder of 1 when divided by 2?"
how does the human brain come up with an answer......
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Mermaid
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Re:Tower of Brahma
« Reply #13 on: 2004-02-28 07:19:07 » |
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Quote from: Mermaid on 2004-02-28 07:05:23
ok..just because you spent so much time on it..
here goes:
(8+/8*(8*8*8--8 = 1000
(8888-888)/8=1000
[(88-/0.8] * [8+(8+/8] = 1000
8[(8*+(8*]-8-8-8 = 1000
[8(8+-(8+8+/8]/8 = 1000 |
good grief!! i did not put up those goofy smiley faces!!! i smell a conspiracy, i tell you...A CONSPIRACY...
and I think Dr.Sebby has something to do with those disgusting smileys
let me try again
(8+8 )/8*(8*8*8-8 )-8 = 1000
(8888-888 )/8=1000
[(88-8 )/0.8] * [8+(8+8 )/8] = 1000
8[(8*8 )+(8*8 )]-8-8-8 = 1000
[8(8+8 )-(8+8+8 )/8]/8 = 1000
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DrSebby
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RE: virus: Re:Tower of Brahma
« Reply #14 on: 2004-02-28 18:50:16 » |
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...i recently attended a smiley symposium in newark. mermaids name was 8th
on the list of guest speakers. her topic; "the Britney Spears Smiley (aka.
oops i did it again)". isnt it obvious that one who despises a thing so,
would turn out to be the most pathological progenator of that thing? keep
your eyes keen with a mermaid...let not the allegory of the mermaid be lost
on you.
DrSebby.
"Courage...and shuffle the cards".
----Original Message Follows----
From: "Mermaid" <hidden@lucifer.com>
Reply-To: virus@lucifer.com
To: virus@lucifer.com
Subject: virus: Re:Tower of Brahma
Date: Sat, 28 Feb 2004 05:19:07 -0700
[quote from: Mermaid on 2004-02-28 at 05:05:23]
ok..just because you spent so much time on it..
here goes:
(8+/8*(8*8*8--8 = 1000
(8888-888)/8=1000
[(88-/0.8] * [8+(8+/8] = 1000
8[(8*+(8*]-8-8-8 = 1000
[8(8+-(8+8+/8]/8 = 1000
good grief!! i did not put up those goofy smiley faces!!! i smell a
conspiracy, i tell you...A CONSPIRACY...
and I think Dr.Sebby has something to do with those disgusting smileys
let me try again
(8+8 )/8*(8*8*8-8 )-8 = 1000
(8888-888 )/8=1000
[(88-8 )/0.8] * [8+(8+8 )/8] = 1000
8[(8*8 )+(8*8 )]-8-8-8 = 1000
[8(8+8 )-(8+8+8 )/8]/8 = 1000
----
This message was posted by Mermaid to the Virus 2004 board on Church of
Virus BBS.
<http://virus.lucifer.com/bbs/index.php?board=61;action=display;threadid=29971>
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