OT - Interesting Mind Teaser

[Gramps]

[ QUOTE ]
Me personally, a friend at work gave me this to chew on, I spent an hour or 2 at work mulling it over when I had a chance, thought about it on the way home from work, another 45 minutes or so, thought about it when falling asleep at night, another half hour or so, let my subconcsious work on it while sleeping and then on the way to work the next day it finally came to me.


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Me too - sometimes I can't get this kind of sh-t out of my head until I think I have it figured out...

[Gramps]

Within your first two weighings, you can narrow the irregular stone down a group of 3 stones or less, and know whether the irregular one is too light or too heavy. Once you get to that point, it's easy to figure out which stone it is on the 3rd weighing.

That, and the first weighing is 4 vs. 4 (because of the fact that you don't know if the irregular stone is lighter or heavier, going 6 vs. 6 gives you zero information, etc.).

I'll try and post an easy-to-read answer later this afternoon (someone may have posted the correct answer, but I'm hungover and it's hard to tell).

[Gramps]

Comment in white:

<font color="white"> Yeah, your step when the two sets of 4 balance is the trick. How to rearrange the stones on the 2nd weighing so that you narrow it down to a group of 3 (or 2), and know whether it's heavier or lighter is the key. Taking 3 normal stones and switching them with 3 from one side, then "flipping" that 4th stone with one from the other side is what took me so damn long to figure out on this one (You've already narrowed it down to 8, that splits it up into groups of 2, 3, and 3 and lets you know which group it's in, and whether it's too heavy/too light). That's the funky step that gives you the requisite information to figure out the rest with just one more weighing.</font>

[Scuba Chuck]

I haven't read a single post yet, but, can I rub a magic genei and get one more use on the scale? I'm still working on this... (and not looking).

[curtains]

Misread question .... rigged.

[Scuba Chuck]

Ok, I'm going to start with the lucky route first (again, I haven't read a single subpost yet).

Measurement 1:
Split into 3 sets of 4 rocks. Weigh two sets against each other. If you are lucky, they will be even, thus indicating that the "odd" rock is one of the 4 remaining rocks.

Measurement 2:
Choose any two rocks and weigh. If you're lucky they will not be even, and you'll have figured out which one of two it is. Keep the rock that is heavier, and weigh it against any of the other rocks.

Measurement 3:
If the heavier rock is even with the last measurement, you'll know the "odd" rock is the one not measured here, and it is lighter than the rest.
Edit: I should add if this last measurement is not even, the "odd" rock is heavier.

Ok, now I have to figure out how to do this if Measurement one is not even. [img]/images/graemlins/tongue.gif[/img] (still not reading)

[ilya]

I hate this problem. It ruined a perfectly good night out with friends for me once.

[lacky]

this may be the most -ev post I've read since the damn paper throwing game post. thanks gramps......

[ClockWyze]

I think I got it.

Should I post it?

[Gramps]

[ QUOTE ]
I think I got it.

Should I post it?

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I think durron posted it about as succinctly as you can (and in white so as not to give it away if people don't want to see it...)