1. Bob tells the truth on only one day of the week.
2. One day he said: "I lie on Mondays and Tuesdays."
3. The next day he said: "Today is either Thursday, Saturday, or Sunday."
4. The next day he said: "I lie on Wednesdays and Fridays."

On which day of the week does Bob tell the truth?

The statements in lines two and 4 can not both be true (they are made on different days and Bob only tels the truth once a week). Therefore Bob must tell the truth one of those four days and, in any case, lies on Thursday, Saturday an Sunday (the other three days). This being the case the statement in line three can not be made on any of those three days since it would be true.

Since the second day can not be Thursday, Saturday or Sunday, it must be monday, tuesday wednesday or friday. THerefore the first day must be either Sunday Monday Tuesday or THursday

But the first day can not be THursday b/c then the first adn last statements (which can not both be false becasue that would cause there to be at least two days when Bob told the truth) would both fall on days when Bob lies

That leaves Sunday Monday and tuesday for the first day

THis leave 5 possibilites
a)Sunday is the first day and Bob is lying that day
b)Monday is first day and Bob is lYing that day
c)Monday is first day and bob is telling the truth
d)Tuesday is first day and Bob is lying
e)Tuesday is first day and Bob is telling the truth.

c and e are eliminated because the statemetn "I lie on Mondays and Tuesdays" can't be true on Monday or Tuesday.

since this leaves no option where Bob can be telling the truth on the first day that means two things 1) the third day must be his truthful day and (since the statement on teh first day is false) His truthful day must be Monday or Tuesday.

The only possible first day to allow teh third day to be Monday or tuesday is Sunday so Bob tells the truth on Tuesday

Posted by FatBoy on 2003-08-15 08:58:07