From: Tim.Epstein@f526.n635.z3.fidonet.org (Tim Epstein)
Newsgroups: rec.puzzles
Subject: Logic Puzzle
Message-ID: <721041158.AA07433@csource.oz.au>

G'day. 
 
As every puzzle I've read here so far seems to be of the 
mathematical type, I thought I'd through in a logic puzzle. 
(Apologies if it has already been posted - I'm new here) 
 
Which of the following 5 sentences are true?
 
a) It is not the case that 2 consecutive sentences are both false. 
b) There are fewer false than true sentences. 
c) It is not the case that 3 consecutive sentences are all false.
d) It is not the case that 2 consecutive sentences are both true. 
e) There are exactly 3 false sentences. 
 
Have fun,
  Tim
 * Origin: I am serious ... and don't call me Shirley. (3:635/526)


From: dcarroll@oucsace.cs.ohiou.edu (Dana Carroll)

This puzzle is not solvable!  My reasoning is as follows:

1) Assume (a) is false.  If (b) is true, then either 
   1.1 (c) and (d) are false, which contradicts (b), or
   1.2 (d) and (e) are false, which also contradicts (b).

2) If (a) is false, then (b) must also be false.  But then
   2.1 one of (c), (d), (e) must be false.
       2.11 assume (e) false.  Then one of (c), (d) also false.  But
            2.111 (c) false implies (d) true, but then (c) is true.
            2.112 (d) false is an immediate contradiction.
       2.12 then (e) must be true.
            2.121 (c) false implies (d) true.  (e) also true contradicts (d)
            2.122 (d) false is an immediate contradiction.

3) So, (a) must be true.  Then either (b) is True of false.
   3.1 (b) true.  Then two of (c), (d), (e) alse true.
       3.11 (c), (d) true contradicts (d)
       3.12 (c), (e) true contradicts (e)
       3.13 (d), (e) true also contradicts (e)
   3.2 So (b) must be false.  Then at least two of (c), (d), (e) also false.
       3.21 (e) false implies (c), (d) false contradicting (c)
       3.22 So (e) true and thus (c), (d) false, contradicting (e)!


So (a) can be neither true nor false!

Did I do something wrong?
  --Dana


From: mclean@itd.nrl.navy.mil (John McLean)

(d) is true; the rest are false.  In other words, the following 5 assertions
are true:

a) 2 consecutive sentences in the puzzle are both false. 
b) There are more or an equal amount of false than true sentences in the puzzle. 
c) 3 consecutive sentences in the puzzle are all false.
d) It is not the case that 2 consecutive sentences in the puzzle are both true. 
e) There are either more than 3 or less than 3 false sentences in the puzzle. 

John McLean