6E   Wednesday  JP    Name:                                              

JP:    Choose one of the following logic problems to solve -- show all your work!

Alice, Betty, Cindy, Debra and Emily are good friends. However, only two of them are really honest, they always tell he truth. The other three girls sometime are honest and sometimes are not. When they were asked about who was a liar. Here are the answers from them: 1. Alice said: Betty is not a lier. 2. Betty said: Cindy is a liar. 3. Cindy said: Debra is a liar. 4. Debra said: Emily is a liar. 5. Emily said: Betty is a liar. 6. Alice said: Emily is not a liar. 7. Emily said: Cindy is a liar. Would you find out which two girls are honest? (28)

There were 2 tribes living on an island. The east tribal people always tell a lie. The west tribal people always tell the truth. Alan and Bryan came from the same tribe. However, we do not know which tribe they came from. When they were asked the marital status, Alan said: “Both of us are married.” But Bryan said: “I am not married”. Are they really married? (32)

Jim and Henry were waiting for the movie to start in the theater. Since they met a lot of their old frields outside of the theater. Jim told Henry: I know one fact, at least there are two people in this theater who has the same number of friends, including zero number of friends. Henry was so surprised he made that conclusion. He said: how can you prove what you just said was true? Jim said: Sure I can. Jim did prove to Henry he was correct. How did Jim prove that was true? (23)

A horse, a donkey and a camcel were stolen. 3 suspects got caught: Robert, Scott and Tommy. All we know that each person stole one animal, but we do not know who stole which. Here are the investigation statements. Robert said: Tommy stole the horse. Scott said: Tommy stole the donkey. Tommy said: They both were lying. I did not steal the horse or the donkey. Later on, the police found out the man who stole the camel told a lie. The man who stole the horse told the truth. Can you find out who stole which? (22)

After an I.Q. competetion, three men got the same highest score. They decided to have another little test to determine who will be the champion. On top of their foreheads, each person has either a black or white sticker. Each person can see the other peoples stickers but not their own sticker. If any one sees a black sticker on ones forehead, he should raise his hand. If he knows what color of his sticker is, he can speak out and he win the championship. After they started, everybody rasied their hands immediately. After a few seconds, one of them spoke out and won the championship. How did he know the color of his sticker and what is the color of his sticker? (21)

George and Harry enjoy creating and solving puzzles. They also enjoy playing card games. On one occasion, George was shuffling the cards, a standard deck, when three cards fell out and landed face-down on the table. George picked up the cards and was about to return them to the deck when he noticed an interesting fact about them. He said, "I have three cards here, Harry. As luck would have it, if I take the numerical value of each card and multiply the three values together, the result equals my lucky number. The highest card is a seven. What are the other two cards?" Harry considered the problem for a few seconds and replied, "I suppose that an ace has a value of one, so each of your other two cards has a value lower than seven and possibly as low as one, right?" "Right," confirmed George. "Well," added Harry, "you haven't told me what your lucky number is, so I could only guess what the two cards are. I need more information to work it out." "I see your difficulty," replied George, "so I will give you one more clue: the lowest card is a spade." Harry pondered the problem again for a while, and then correctly identified the two cards. What were they? (29)

5 Sailors and a monkey landed on an island in the southern Pacific Ocean. They found a big pile of coconuts. Since they were so tired and it was getting late, they all went to sleep instead. Allan woke up at night. He wanted to get his share right then. He divided the coconuts evenly into 5 piles, but one coconut was left. He hid one pile for himself and gave the extra one to the monkey. He went back to sleep. Brad woke up (without knowing what had happened) after Allan. He divided the rest of the coconuts evenly into 5 piles, but one coconut was left. He hid one pile for himself and gave the extra one to the monkey. He went back to sleep. Charlie woke up (without knowing what had happened) after Brad. He divided the rest of the coconuts evenly into 5 piles, but one coconut was left. He hid one pile for himself and gave the extra one to the monkey. He went back to sleep. David woke up (without knowing what had happened) after Charlie. He divided the rest of the coconuts evenly into 5 piles, but one coconut was left. He hid one pile for himself and gave the extra one to the monkey. He went back to sleep. Earl woke up (without knowing what had happened) after David. He divided the rest of the coconuts evenly into 5 piles, but one coconut was left. He hid one pile for himself and gave the extra one to the monkey. He went back to sleep. When they all awoke in the morning, they determined to divide the rest of the coconuts evenly into 5 piles. Each sailor got a pile. Again one coconut was left, and they gave it to the monkey. Everybody got one pile. How many coconuts did each person get? (30)