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### 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/
```
Associated Topics:
High School Logic
Middle School Logic

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