Logic Question: The Hard One

[The Armchair]

No, this isn't a re-post

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 an amount different (could be more, could be less) 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 you just lose your ability to walk?

[M2d]

Whip out your junior inspector badge that you got from your frosted flakes when you were twelve and have been carrying around in your wallet ever since. flash it so that he can't tell exactly what it is, then demand your $300 in protection money.

[swimfan]

Take 3 sets of 4. Let's name them A, B and C.

Compare A and B. If equal, you realize C contains the counterfeit chip. Let's take 2 sets of 2 from C. Let's name them C1 and C2. Take the two chips from C1 and weigh against each other. If equal, compare one chip from C1 to one chip from C2 (if not equal, you know the counterfeit). If equal, the counterfeit is the unweighed chip from C2, if not equal it is that chip you're comparing from C2.

If A<>B, use same steps from above example (C) to determine counterfeit chip in 3 steps or less.

[aloiz]

wow this is not easy, but I think I got something. Three weighs of four each.

first weigh: 1,2,3,4 and 5,6,7,8
2nd: 1,2,6,9 and 5,3,10,11
3rd: 11,4,7,6 and 12,1,5,10

Each weigh can go left, right, or equal. Assuming the counterfeit is heavier, the following are the weighs for each number (if the counterfeit is lighter just change all the lefts to rights):
1: left, left, right
2: left, left, equal
3: left, right, equal
4: left, equal, left
5: right, right, right
6: right, left, left
7: right, equal, left
8: right, equal, equal
9: equal, left, equal
10: equal, right, right
11: equal, right, left
12: equal, equal, right

aloiz

[aloiz]

This is the way I tried first, but if A<>B which set has the counterfeit, A or B?

aloiz

[The Armchair]

The other one is surprisingly easy. This one is incredibly hard. I like the paradoxical elegance. [img]/images/graemlins/smile.gif[/img]

[moondogg]

LOL. I ask this in interviews, but it always bowling balls where one is slightly heavier than the others. I'll have to start using this version (with your permission, of course).

Thanks

[The Armchair]

It's not "mine," per say (but the underlying story is -- modicum of creativity and all, and you have my permission to use it.) However,

do not ask this in an interview.

Not because I don't want you to, but that it's really hard. I've been asking this for almost 10 years now, and I can't give the answer w/o taking notes along the way.

If you want ones that work well in an interview, I'll give you a couple, memory providing.

[moondogg]

[ QUOTE ]

do not ask this in an interview.

Not because I don't want you to, but that it's really hard. I've been asking this for almost 10 years now, and I can't give the answer w/o taking notes along the way.




[/ QUOTE ]

Exactly. During an interview, I don't care what a person CAN do, I want to find their outer-bound, i.e. what they CAN'T do. Obviously just about nobody is going to be able to answer this question completely and correctly in an interview. But if you give them a pen and paper and 10 minutes to fool around with it, you'll get a some sort of a gauge of their problem-solving skills.

Of course, you might offend the person by asking a really hard question that they probably can't answer. That makes the rest of the interview easy: I'm definitely not going to hire this emotional tissue paper, so we can talk about the weather or sports for the remaining 5 minutes of the interview.

[The Armchair]

I'm not going to give the answer to this one, or at least not for a few days. I will tell people why they are wrong, though.