Logic Puzzles, Paradoxes and Silliness


Silly Syllogisms

Cats have nine lives

No cat has eight lives.
One cat has one more life than no cat.
Therefore, one cat has nine lives.

God is a bat

God is love
Love is blind
Bats are blind
Therefore, God is a bat

My dog is special

Some dogs are brown
My dog is brown
Therefore, my dog is some dog. 

Puzzles

Sums and Products

There are two numbers not necessarily distinct. Mr. P knows the product of the two numbers and Mr. S knows the sum of the two numbers. The following dialogue ensues:
Mr. P 'I don't know what the two numbers are.'
Mr. S 'I know you don't know. I don't know what they are either.'
Mr. P 'Now I know what they are.'
Mr. S 'Now I know too.'
What are the numbers ?

Lions and Unicorns

There were once two beasts of the forest, a lion who always lied on Mondays, Tuesdays and Wednesdays, but otherwise told the truth, and a unicorn who always lied on Thursdays, Fridays and Saturdays, but otherwise told the truth. A chance encounter between the two animals caused them to announce in unison "Yesterday, I was lying!"
Which day was it? 

Paradoxes

 

 
(1) There are three statements in this box. 
(2) Exactly two statements in this box are false. 
(3) 2 + 2 = 5 

  1. (1) is clearly true.
  2. If (2) is true then since (1) is true (2) must be false. So (2) is false.
  3. There are either 3, 2, 1, or 0 false statements in the box.
  4. There are not 3 by 1.
  5. There are not 2 by 2.
  6. There are not 0 by 2.
  7. Therefore by 3 - 6 there is 1 false statement in the box which must be 2.
  8. So (3) is true, i.e., 2 + 2 = 5.