X and Y are two different integers, greater than 1, with sum less than or equal to 100. S and P are two mathematicians; S knows the sum X+Y, P knows the product X*Y, and both are perfect logicians. Both S and P know the information in these two sentences. The following conversation occurs: S says "P does not know X and Y." P says "Now I know X and Y." S says "Now I also know X and Y!" What are X and Y?
April 24, 2015
April 16, 2015
Albert and Bernard just met Cheryl. “When’s your birthday?” Albert asked Cheryl. Cheryl thought a second and said, “I’m not going to tell you, but I’ll give you some clues.” She wrote down a list of 10 dates: May 15, May 16, May 19 June 17, June 18 July 14, July 16 August 14, August 15, August 17 “My birthday is one of these,” she said. Then Cheryl whispered in Albert’s ear the month and only the month of her birthday. To Bernard, she whispered the day, and only the day of her birthday. “Can you figure it out now?” she asked Albert. Albert: I don’t know when your birthday is, but I know Bernard doesn’t know, either. Bernard: I didn’t know originally, but now I do. Albert: Well, now I know, too! When is Cheryl’s birthday? ANSWER! Lets first analyze all the given birth dates. The dates can be easily viewed as
April 13, 2015
April 10, 2015
Which of the following statements are true and which are false? 1. Only one of the statements is false. 2. Exactly two of the statements are false. 3. Only three of the statements are false. 4. Exactly four of the statements are false. 5. All five of these statements are false.