Mathematics: All Classes: Wednesday 3.29.06 Period 1

[dorky-broots.livejournal.com]

Broots looked like he had just gotten into an argument with his laptop when the class came in. "Morning everyone. If you're not awake, coffee is in it's usual place.

Beginners, you guys are going to work on a couple interesting problems.
Problem one: John has an identical twin brother. Either John or his twin always lie. What three word question could you ask one of the boys that he will answer either yes or no that will reveal to you if you are talking to John or his twin?
Problem two: So you found out which twin is John. Now, is John the lier?
If you finish early, I have a few more problems that you can do for extra credit.

Intermediate, you guys get tormented by chess today. You have a normal chess board, eight by eight squares, sixty-four squares total. You are to put the numbers 1 through 64, one per square, on the board. The catch? When going from one to two, two to three, etc, you can only move in the same way the horse piece moves. So either two squares up, one right or two left, one down or two left, one up, etc. When you're done, you can use the chess boards to actually play chess."

Comments

Sign In

[dorky-broots.livejournal.com]

And coffee, cookies, chips, and chocolate milk.

Re: Sign In

[anole-x.livejournal.com]

Victor signs in and takes some of all. He's a growing teenager, after all.

Re: Sign In

[cyclopeanmerc.livejournal.com]

Pip signs in and has some coffee and chips.

Re: Sign In

[bruiser-in-pink.livejournal.com]

Molly signed in and took some cookies and chocolate milk. Mmmm, cookies for breakfast.

Re: Sign In

[strongestgirl.livejournal.com]

Pippi signs in and takes coffee.

Re: Sign In

[walter-n-wires.livejournal.com]

Walter signs in, takes some of everything, and adds the chocolate milk to his coffee before sitting down.

Re: Sign In

[kikidelivers.livejournal.com]

Kiki signs in.

Re: Sign In

[apocalypsesoon.livejournal.com]

john signs in

Re: Sign In

[cameronmitchell.livejournal.com]

Cameron signs in.

Beginners

[dorky-broots.livejournal.com]

What's the question?

Re: Beginners

[anole-x.livejournal.com]

After a lot of thinking and some figure-scribbling, Victor's question is, "Does John lie?".

By the end of the period, though, he still hasn't figured out the answer to the second problem.

Re: Beginners

[kikidelivers.livejournal.com]

Kiki puzzles this over for a while, and finally writes out her answer.

"I can solve the problem, but only if I do it in the reverse order. First, I would ask each twin, 'If I ask you if your brother lies, will you say yes?' The brother who answers 'No' to that question is the liar. If I asked 'Does your brother lie?' the truth-telling brother would say, 'yes, my brother lies.' The lying brother would of course lie, and say 'yes, my brother lies.' However, if I ask the first question, the truth-telling brother would say, 'Yes, I would answer yes to that question.' However, the lying brother would have to lie about lying, and he would answer, 'No.'

Once I know that, of course, it's easy to ask the truth-telling brother, 'Are you John?' I can't figure out a way to do this problem in the order presented, though."

Re: Beginners

[strongestgirl.livejournal.com]

My three word question would be, "Are you a man?"

The brother who says "No" is a dirty dirty fibber.

After that I'll ask the one who admits to being a man if he's John.

Re: Beginners

[bruiser-in-pink.livejournal.com]

Molly just sat there and wondered what this had to do with math.

Re: Beginners

[cameronmitchell.livejournal.com]

"What colour is your hat are too many words," Cameron sighed.

Re: Beginners

[cyclopeanmerc.livejournal.com]

Pip scratches his head and shrugs. "I guess I'd have to say "Is John honest?" Unless I can use French."

Intermediate

[dorky-broots.livejournal.com]

And the key word is...?

Re: Intermediate

[walter-n-wires.livejournal.com]

Walter sits with the chessboard and spends the class period working out the problem.

By the end of the class period, he still hasn't figured it out. He's a butler, not a mathematician, dammit.

Re: Intermediate

[dorky-broots.livejournal.com]

Broots draws in the number one for him in the upper left hand square. "Think circles. Try this problem a bit later and see if you can come up with a solution for Friday."

After Class

[dorky-broots.livejournal.com]

If you need Broots, he's apparently deep in conversation with his laptop.

Re: After Class

[anole-x.livejournal.com]

"Excuse me, sir?"

Re: After Class

[dorky-broots.livejournal.com]

Broots blinked. "Um, Broots is fine. Please. Since I might be younger than you anyway. Yeah?"

OOC

[dorky-broots.livejournal.com]

Beginners: Does John lie? Is John truthful? Both work. Try to work out the explanation of why, it's rather fun. :)
Intermediate: You start in one of the corner squares and then go in circles around the board. I can never get it down right, though.

Re: OOC

[anole-x.livejournal.com]

Sorry, but my brain is totally breaking over this one. Is there a site or something I could visit that'll be able to explain the liar thing to me in, like, 8-year-old terms? Because, ow...

Re: OOC

[threeweapons.livejournal.com]

Sorry, I plucked it out of one of my many math puzzle books. The John one right?
Let's take question Is John truthful?
You ask Twin A. He says yes. If he is the truthful twin, then John is truthful and since he is the truthful twin, he is John. If he is the lying twin, then John is not truthful BUT he is the lying twin so he is still John.
You ask Twin A. He says no. If he is the truthful twin, then John is a liar, but he is truthful so Twin B is John. If he is the lying twin, then John is truthful BUT he is a liar, so Twin A is still John.
Summary: If the twin says yes, he is John, if he says no, the other boy is John.