Fun logic puzzles

1. Stephen was looking at a photo. Someone asked him, "Whose picture are you looking at?" He replied: "I don't have any brother or sister, but this man's father is my father's son." So, whose picture was Stephen looking at?

2. There was a robbery in which a lot of goods were stolen. The robber(s) left in a truck. It is known that : (1) Nobody else could have been involved other than A, B and C. (2) C never commits a crime without A's participation. (3) B does not know how to drive. So, is A innocent or guilty?

3. Suppose there is this little town with a finite numer of people: (1) No two inhabitants have exactly the same number of hairs. (2) No inhabitant has exactly 409 hairs. (3) There are more inhabitants than there are hairs on the head of any inhabitant. So, what is the largest possible number of inhabitants in that little town?

4. The following logical deduction test was reported to have been one of the questions given for 14-year-olds in the Singapore and Asian Schools Math Olympiad. [Read more]

Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates.

• May 15, May 16, May 19
• June 17, June 18
• July 14, July 16
• August 14, August 15, August 17

Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.

Then Albert said: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.

Bernard: At first I don’t know when Cheryl’s birthday is, but I know now.

Albert: Then I also know when Cheryl’s birthday is.

So when is Cheryl’s birthday?

5. This puzzle is from the late logician and mathematician Raymond M. Smullyan: A dealer bought an article for $7, sold it for $8, bought it back for $9, and sold it for $10. How much profit did he make? answer