Batch 3 - Class 183 - Logic Problems

• (MartinColl Page 203) You know how to place 8 queens on a chessboard so that no two attack each other. Can you place 10 queens so that each queen attacks exactly one other queen?
• Answer: You can simplify by first solving for 6 queens on 6x6 board

• Cheryl's Birthday Problem - Cheryl's birthday is on one of the following days - May 15, May 16, May 19, June 17, June 18, July 14, July 16, August 14, August 15, August 17.
• Cheryl tells Albert and Bernard separately the month and the day of her birthday respectively. Then following conversation takes place
• Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard doesn’t know too.
• Bernard: At first I didn’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?
• Solution: It is clear that we’ll try to eliminate the 10 choices and finally narrow down to one correct answer based on the arguments given by Albert and Bernard. So let’s eliminate the choices argument by argument.

  Argument 1:  Albert says, I don’t know when Cheryl’s birthday is, but I know that Bernard doesn’t know too.

  If we look at the dates we observe that if May 19 or June 18 were Cheryl’s birthday then Bernard would have known it instantly because there are only one date with 18 and 19. If Albert knows this fact then he is either told July or August Month. Hence all the dates of May and June are eliminated.

  Now the remaining choices are

  July

  14

  16

  August

  14

  15

  17

  Argument 2: Bernard says, At first I didn’t know when Cheryl’s birthday is, but I know now.

  This eliminates July 14 and August 14 because If Bernard know the exact date, it can’t be 14 as that will create ambiguity between July 14 and August 14.These two dates are eliminated.

  The remaining choices are

  July

  16

  August

  15

  17

  Argument 3 Albert says, Then I also knows when Cheryl’s birthday is.

  If Albert knows the date then it has to be JULY 16 because, in August there are two choices and Albert can’t be sure of his decision. If Albert is absolutely sure then answer is July 16 and all the august dates are eliminated.

  Answer: July 16

  
  
• Gender Ratio: If parents are neutral to having a boy or a girl, what is the expected ratio of boys and girls in the society?
• Answer: 50%
• Now, let us assume that all parents really want to have a daughter. So they keep having kids till they have their first daughter, and then they stop having kids. What is the gender ratio in the resultant population?
• Do you expect it to be in favor of girls or boys?
• Lets simulate using heads and tails - do an experiment for 20 repetitions
• Analyze this probabilistically
• Answer: Its still 50%. Why? Why is the preference for having a girl not increasing the ratio of girls?
• Note that no one has more than 1 girl... Where as they can have many boys in their wait for a girl.

• Seven Envelopes: There are seven envelopes numbers 1 through 7, and one of those has the winning lottery ticket. Can you find out which one. Clues are as under, but two of the clues are false:
1. The main prize can be found in an envelope with an odd number label.
2. The main prize can be found in one of the following envelopes: 2, 3, 6 or 7.
3. The main prize can be found in an envelope whose number is larger than 3.
4. If Clue 1 is false, then Clue 3 must be true.
5. Both Clue 2 and Clue 4 are true.

• Solution: Envelope 5.
• Note that if Clue 5 is true, then so are 2,4. Then 1 and 3 must be false, but that is not possible because if 1 is false then 3 is true. So 5 must be false. Then one of 2 or 4 is false as well. If 4 is false, then 1 and 3 must be false, which is not possible. So 4 is true and 2 is false. 1 and 3 are true as well. These three then mean that the winning ticket must be in envelope 5.

• A person has 3000 bananas and a camel. The person wants to transport maximum number of bananas to a destination which is 1000 KMs away, using only the camel as a mode of transportation. The camel cannot carry more than 1000 bananas at a time and eats a banana every km it travels. What is the maximum number of bananas that can be transferred to the destination using only camel (no other mode of transportation is allowed).
• Solution: 533 1/3