A sheet of paper has statements numbered from 1 to 40. For all values of n from 1 to 40, statement n says: 'Exactly n of the statements on this sheet are false.' Which statements are true and which are false?

a) The even numbered statements are true and the odd numbered statements are false.
b) The odd numbered statements are true and the even numbered statements are false.
c) All the statements are false.
d) The 39th statement is true and the rest are false.

• In such cases there are some thumb rules:
  At least: First half of the statements are true, 2nd half are false.
  Exactly: The (N-1)th Statement is true.
  At most: All the statements are true.
  
  so in that case: Exactly the 39th statement is true and the rest are false.
  answer: d)
• 13 years agoHelpfull: Yes(14) No(1)
• only option 1 fits the bill as for odd and even we have 37 are false 39 are false which is in contradiction and same is the case with 36 and 38.
  
  also not all are false
  
  so only option 1 is correct
• 13 years agoHelpfull: Yes(3) No(7)