Brain teaser-type thingie

A

Apollo

Guest
I was posed this question elsewhere, and the solution keeps niggling at my mind, but I can't wrap my brain around it:

You have 12 marbles, and a simple scale (where you can put two things or groups of things on it and find out what weighs more, but you can't figure out the exact weight). 11 of the marbles weigh the same, and the other is different. You don't know whether it is lighter or heavier than the others. You can perform only 3 weighings to find out which is the different marble. How do you do it?
 
H

Hetemti

Guest
6 on pan one, 6 on pan two. Eliminate the lighter half.
3 on pan one, 3 on pan two. Eliminate the lighter half.
1 on pan one, 1 on pan two, 1 set aside. Iff balance is unequal, eliminate the lighter half, remainder is the heavy one. Iff both are equal, the unweighed marble is the heavy one.
 
S

sageridder

Guest
put 6 on each tray,take the 6 from the lite group and put them on the table.(you could choose heavy dosn't matter)
put 3 from the lite group in the empty tray.If they balance this your normal group,and the odd one is heavy.If they do not the ones on the table are normal and the odd one is lite.
 
A

Apollo

Guest
Hetemti: You don't know that the odd marble is heavier than the others; all you know is that it's different. It could be lighter than the others. So eliminating the lighter half doesn't work.

Sageridder, it's not enough to find out whether it is heavy or light, you need the specific marble.

I just now managed to figure it out, but I'll leave this up here and see who else can get it before I post the answer. It's rather complicated.
 
H

Hetemti

Guest
You underestimate my powers. If it's not heavier, it'd better get heavier, or I'll make it heavier.
 
I

Istanbul

Guest
Curses...I can get it down to one of two about 12,000 different ways, but not with certainty down to 1.
 
L

Lotus Mox

Guest
WOW this is a pretty hard one, but I think I found a solution (took me 10 minutes to find it out :( ) :

it's big beware ;)

I call the marbles:
ABCDEFGHIJKL.
X are marbles which can't be the searched one.

/ means the left side weighs more, \ means the right side does, - means equal.

you weigh:

ABCD ? EFGH

if it's / (or \) you weigh:
ABGH ? EXXX

if it's / (or \) it means, the marble has to be ABE (i.e. it doesn't have switched place)

if it's - the marble has to be CDF

if it's \ (or /) the marble has to be GH (i.e. it switched place)

this narrows it down to 3 marbles, 2 marbles are cakewalk.

if you have 3 marbles and have already weighed them (let's pretend ABE contains one) like this ABXX / EXXX (from the first weighing)

you weigh A ? B

if it's /, A is the searched marble.
if it's \, B is the searched marble.
if it's -, E is the searched marble.

same for all the other cases.

Now if the marbles are in IJKL you weigh:

IJ ? KX

you should be able to find out how this will result in the searched one :)
 
S

Spiderman

Administrator
Staff member
This puzzle appears in several fantasy books, the one I can remember is from the Incarnations of Immortality series by Piers Anthony :)
 
R

Ransac

CPA Trash Man
Wow, I haven't read that puzzle in about 4 years.

Here's a new puzzle: Who hid the donkey?



Ransac, cpa traah man
 
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