[CFUW 81 - Locked to Ty Lee and Nerdlinger of the Water Tribe]

[head_overheels]

Hey, Sokka, look, we've got a private place all to ourselves~

Comments

[immunostasis.livejournal.com]

Hey there, sweetie.

Here's your problem the two of you have to figure out.

You have twelve coins. You know that one is fake. The only thing that distinguishes the fake coin from the real coins is that its weight is imperceptibly different. You have a perfectly balanced scale. The scale only tells you which side weighs more than the other side.

What is the smallest number of times you must use the scale in order to always find the fake coin?

[head-overheels.livejournal.com]

... Sokka, please get here quick.

[head-overheels.livejournal.com]

... wait, do we only get one guess or do we get multiple guesses?

[immunostasis.livejournal.com]

Depends... really. On how you base your answers on.

[o-sarchasm.livejournal.com]

I'm here, I'm here. Give me a minute.

[o-sarchasm.livejournal.com]

I know this one! I'm guessing we get extra points or something for a good explanation, right? So! First you separate the coins into two groups of six.

1 1 1 1 1 1
2 2 2 2 2 2

Those are the two sets. Weigh 1 1 1 against the other 1 1 1. If the scale tips in either direction, you know the fake coin is one of those six. And that means that the coins in the other set are all normal -- that's your control group.

Are you getting this so far, Ty Lee?

[head-overheels.livejournal.com]

*... o-oh that's your "I'm being a huge nerd" smile isn't it*

Uh-huh! Go on.

[o-sarchasm.livejournal.com]

Okay, I'm working under the assumption that all of the coins in group 2 are real, and the fake coin is somewhere in group 1. Either way, the number of times you use the scale is the same.

Weigh the first three coins from group 1 against any three coins from group 2. If they weigh the same, the fake coin is one of the other three coins in group 1. That's how you figure out which group of three the fake coin is in. Forget about the control coins from group 2 -- weigh any coin from your group of three against any other coin, and that'll tell you which one is the fake. If the two you compare weigh the same, the third coin is the fake. We don't know if the fake coin is heavier or lighter, so we can't tell which one is the fake if it's one of those two. But that doesn't matter! The answer is three. You only need to use the scale three times!

[head-overheels.livejournal.com]

Awesome, Sokka! I'd congratulate you with like a kiss on the cheek or something but then you'd just spaz again.

[immunostasis.livejournal.com]

Wow, you really are the class nerd.

[head-overheels.livejournal.com]

There's a reason why I said it should be him right off the bat, y'know?

[immunostasis.livejournal.com]

I see.

[o-sarchasm.livejournal.com]

I'm taking that as a compliment.

[o-sarchasm.livejournal.com]

All you need to say is, "I'm glad your occasional nerdiness swooped in to save the day, Sokka. You're the best clue partner ever!"

[head-overheels.livejournal.com]

I'm glad your total nerdiness swooped in to save the day, Sokka! You're the best clue partner ever~ ♥

[immunostasis.livejournal.com]

It... is?

[immunostasis.livejournal.com]

hahaha, anyway, you deserve this:

George, who didn't give Billy an A, didn't teach physics. Amanda didn't teach history.

[head-overheels.livejournal.com]

Aww, thanks! ♥

[o-sarchasm.livejournal.com]

Thank you. I am, aren't I.

[o-sarchasm.livejournal.com]

...Oh I see what you did there.