A little Problem...

jeff hammond

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 ?

pilou

@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

remus

@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:

Ecuadorian

@remus said:

-a disc must always be placed on a larger disc.

...or directly on the base.

remus

Updated

pilou

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!

jeff hammond

can i just answer 'it's going to take forever' ?
that is a huge huge number that i don't really know how to write

i 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.

remus

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.

remus

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

jeff hammond

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

jeff hammond

@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

remus

Very sensible

Daniel

204 minutes

remus

howd you get that?

pilou

is it not the famous Hanoï tower?

jeff hammond

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
31

which 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..

Page not found – Welcome to the Petting Zoo

(www.petting-zoo.org)

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?

Ecuadorian

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.

remus

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

jeff hammond

@ecuadorian said:

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.

haha, okay Miguel.. the check is in the mail!

pbacot

@remus said:

Well done people, its not a trick question: 2 is the correct answer as ecuadorian said (and the scales are the 1st type you posted jeff.)

edit: doh, put 3 instead of 2. Corrected.

Wait, thought it was 2.