Lies and Truths... What Day Is It?Date: 04/09/2002 at 20:14:01 From: Renee Subject: 7th grade math word problem Jim tells lies on Friday, Saturday, and Sunday. Fred tells lies on Tuesday, Wednesday, and Thursday. Both tell the truth other days. If they both say "I lied yesterday," what day is it? I have made a chart, but I'm still stuck. Mon Tue Wed Thur Fri Sat Sun JIM T T T T L L L FRED T L L L T T T Date: 04/10/2002 at 12:40:56 From: Doctor Ian Subject: Re: 7th grade math word problem Hi Renee, This is an excellent start! The table you made will be essential in working out the solution. I'm going to make one little change to it, which is to include Sunday twice: Sun Mon Tue Wed Thu Fri Sat Sun Jim L T T T T L L L Fred T T L L L T T T This way, for any given day I can easily see what the situation was on the day before. In particular, when when I'm thinking about Monday, I don't have to look all the way to the other end of the table. Does that make sense? Can we make up a description, or a pattern, that describes what has to be going on for both Jim and Fred to say "I lied yesterday" on the same day? Jim is either telling the truth, or he's lying. If he's telling the truth today, and he says he lied yesterday, then he must have lied yesterday. On what days can this happen? (That is, on what days does Jim have a T preceded by an L on the previous day?) If you'll look at the table, you'll see that it can happen ONLY on Monday. If Jim is lying today, and he says he lied yesterday, then he must have told the truth yesterday. On what days can this happen? If you'll look at the table, you'll see that it can happen ONLY on Friday. So whatever is going on with Fred, we've already narrowed it down to Monday or Friday. Can you take it from here? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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