A little Problem...
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really? the way i see it, you can always find the the heavy one in 3 tries.. you mind showing the 1 out of 24 when it wouldn't work?
further, using a different starting technique using 12 objects (5vs5), it's possible to find the oddball in 2 tries.. sometimes (17% chance of doing it 2)
let's say the heavier object is #11..
place 1,2,3,4,5 on one side and 6,7,8,9,10 on the other.. they weigh the same so that eliminates 1-10
place #11 on one side and #12 on the other..
11 weighs more so you've found it in 2 weighings.
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Annsi, sorry, typo. 2 is the right answer to the original question
Ive got another one for you.
(This problem is an extended case of the above problem.)
The aim is to transfer all the discs from one pole to another without placing a larger disc on a smaller disc at any point.
The rules for moving the discs:
-you can only move 1 at a time,
-a move consists of moving one disc from one pole to another without changing the position of any other discs;
-a disc must always be placed on a larger disc or directly on the base.If i can move the discs at a rate of 10 a minute, how long would it take me to complete a puzzle with 64 discs?
For additional cool points, can you prove your answer? and how does adding a 4th pillar effect the solution?
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@remus said:
If i can move the discs at a rate of 10 a minute, how long would it take me to complete a puzzle with 64 discs?
wait, you didn't mention what the finished puzzle should be.. do you mean start with the picture and move the stack to a different pole following your guidelines?
[edit1]oh wait.. 3 poles, all 64 discs are off the poles, then build one stack on one pole?
[edit2] ok, i think i got it now
.. start with a stack of 64 discs on one pole then transfer them to another pole ? -
@Jeff
Of course yes, it's just the methodology
In the real world you will be obliged to make all combinaisons first till find a solution and say this is the false object!
Try it in the real world and you will see that i am right
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@unknownuser said:
wait, you didn't mention what the finished puzzle should be.. do you mean start with the picture and move the stack to a different pole following your guidelines?
Thats it, the aim is to move all the discs to another pole following the rules, so for 2 discs the solution would look like this:
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Updated
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That is more interresting
You can win 2 millions $ for make a "little" puzzle
But now make speedy answer : 31 12 2009 end first step of the game!
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can i just answer 'it's going to take forever' ?
that is a huge huge number that i don't really know how to writei did find a method to obtain the answer though
basically,
2disc = 3 moves
3disc = 7
4disc = 15
5disc = 31
6disc = 63
etc..following that sequence, 7discs = 127 then 8 = 255
i'll try to get it better than that though. -
Good start jeff
Youve got what we in the business call a recursive solution i.e. you can find n+1 if you know n.The general solution should be fairly easy to find from there.
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Your a factor of 100 out, you can make 10 moves a minute whereas i guess you took a move takes 10 minutes. Otherwise correct though
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well, here's the answer i'm going to go with but this stuff is over my head.. i like the practical everyday logic puzzles much better
184,467,440,737,095,516,150 minutes
[edit] hmm.. maybe that's 10 minutes too long? i guess you don't have to wait 10 minutes before making the very first move.
[edit2] oops agian.. i figured it as if you make one move every 10 minutes instead of 10 per minute..
so maybe it's more like
1,844,674,407,370,955,161 minutes...and 30seconds -
@remus said:
Your a factor of 100 out, you can make 10 moves a minute whereas i guess you took a move takes 10 minutes. Otherwise correct though
right.. i update my post as you were posting yours.
ok, i'm gonna go eat ice cream now
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Very sensible
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204 minutes
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howd you get that?
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is it not the famous Hanoï tower?
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fwiw, the way i figured it out was by physically doing the puzzle in sketchup with 2,3,4 & 5 discs then looking for a pattern..
my results were
3
7
15
31which i realized was the same a 4,8,16,32,64,etc minus 1..
then i had to find a big enough calculator to figure out the rest..i'm sure there's a way to do this using formulas but i'm more of a hands on type
similar math is applied to this question:
would you rather I give you $5000 right now -or- give you a penny right now, 2 pennies tomorrow, 4 pennies the next day etc.. for an entire month?
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Only Bill Gates and a few other chaps have enough spare change to pay the amount you would owe me, Jeff ($10,737,418.23), so I prefer you give me the $5,000 today.
EDIT: I mistook pennies for dollars and 5000 for 500, so I updated my post.
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Pilou, it is indeed the towers of hanoi problem.
In a similar vein there is the wheat and chessboard story: http://en.wikipedia.org/wiki/Wheat_and_chessboard_problem
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