Logic/Math Problem: The Easy Question

[The Armchair]

Given the other question(s), here is my favorite. Well, this one isn't, but the follow up is.

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You're playing 2/4 Hold'em at a card barn. Underground. Illegal. All that fun stuff. Somehow, all your white and red chips turned into greens over the course of the night. (Good for you!) Unfortunately. . . well, let's start from the beginning. Or rather, the beginning of the end.

You have a counter-balance (or a scale, the one Justice holds). You know the type -- a tray on either side, tethered together by some sort of bar. Like, uh, this:



Good?

Good.

You also have 12 -- count 'em, twelve poker chips. All are green and unmarked, and if you try and cash them in at the cage, you'll get your kneecaps broken. Why?

One of them is a counterfeit *gasp*!

Which one? Well, the one that weighs more than the others, of course!

Of course, you didn't know this when you tried to redeem them for your $300. The floorperson takes you into the back room, acting all Grand Inquisitor on you:

"Where'd you get the chips?"
"Tell us and we'll go easy on 'ya!"
"And... where'd you get that weird counter-balance thingy?"

You, of course, have no idea. One too many Seven-and-Sevens.

The floorperson decides that you're honestly ignorant, but decided to have some fun. He puts your counterbalance on the table and lays the 12 chips out directly in front of it. He labels them 1 through 12, and tells you he's going to call the police unless you can help him identify the counterfeit. How? Well, with the scale of course! (Good thing you had it with you.)

Only... that'd be too easy, and he's got you by the . . . yeah, those. He adds a wrinkle: You can only use the counter-balance three times.

How do you find the counterfeit chip?

Or do your just lose your ability to walk?

[1800GAMBLER]

Answer in white:

<font color="white"> Cut 6/6 keep the heavier 6. Do the same with 3/3. Then you have 3 left and one is the heavier one, put any two on the scale, if one is heavier it's that one, if they weigh the same it's the one you didn't put on. </font>

[aloiz]

First weigh six on each side, noting which side is heavier. Then take 1 out from the heavier six and put it aside. Take one from the lighter six (must be a real chip) and add it to the now five. Weigh 3 and 3, keeping track of the added real chip. If both sides are equal you know the counterfeit chip is the one you took out. If the side with the real chip is heavier the third trial is between one of the two remaining chips. If the side without the real chip is heavier take out one of the chips from the heavier side, and weigh the remaining two. If they're equal the one you took out from the group of three is counterfeit, else the counterfeit is the heavier of the two.

aloiz

Edit: Ignore mine, Gamblor's is a much simpler solution

[daryn]

this one is easy, but it's better if you stipulate that the counterfeit chip weighs more OR less than a real one.

[The Armchair]

That'll be the next question. Don't worry [img]/images/graemlins/smile.gif[/img]