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fandomhigh2006-03-29 04:35 pm
dorky-broots.livejournal.com) wrote in fandomhigh2006-03-29 04:35 pm
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Mathematics: All Classes: Wednesday 3.29.06 Period 1
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."
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."
Re: Beginners
"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."