There are two boys participating at an international maths contest in December 2013. One is British and the other is American. They both write their names, the date, and their answers on the paper. The only problem is that they both have the same name and the papers cannot be told apart. What is the date?

Below are four multiple-choice entrance exam questions. Can you find the answers? 1. The answer to Question 2 is: A. B B. A C. D D. C 2. The answer to Question 3 is: A. C B. D C. B D. A 3. The answer to Question 4 is: A. D B. A C. C D. B 4. The answer to Question 1 is: A. D B. C C. A D. B

Mrs. Stotch is a fifth grade teacher. One of her students took her apple. Mrs. Stotch has narrowed the suspects down to Billy, Paige, and Tyler. Each of the students give these statements: Billy: I didn’t do it. Paige: I didn’t do it. Tyler: Paige did it! Mrs. Stotch knows that only one of the kids is telling the truth. Who is telling the truth and who took the apple?

Last week Tom decided to cycle to his grandmother’s house. On the first day, he cycled half of the distance. On day 2, he cycled one half of the remaining distance. On day 3, he cycled three quarters of the remaining distance. On day 4, he cycled 10 miles. On day 5, he cycled two thirds of the remaining distance and on the final day he cycled the remaining 5 miles. How far is it to his grandmother’s house?

Two mathematicians, Tom and Smith are walking down the street. Tom: I know you have three sons. What are their ages? Smith: The product of their ages is 36. Tom: I can’t tell their ages from that. Smith: Well, the sum of their ages is the same as that address across the street. Tom: I still can’t tell. Smith: The eldest is visiting his grandfather today. Tom: Now I know their ages. Do you know the age of the kids?

Two old friends, Jack and Bill, meet after a long time. Jack: Hey, how are you man? Bill: Not bad, got married and I have three kids now. Jack: That’s awesome. How old are they? Bill: The product of their ages is 72 and the sum of their ages is the same as your birth date. Jack: Cool… But I still don’t know. Bill: My eldest kid just started taking piano lessons. Jack: Oh now I get it. How old are Bill’s kids?

A king has 1000 bottles of wine and one has been poisoned. Even a sip of the poisoned wine is enough to kill a person. The king asks the royal jailor to identify the poisoned wine bottle by testing them on the prisoners. It takes up to 24 hours for the poison to take effect. There are unlimited number of prisoners at the jailer’s disposal. What is the minimum number of prisoners the jailer needs to identify the poisoned wine bottle in 24 hours?

In a cave there is a treasure within a big metal box with a lock on it. There is also a monster in the cave that has two keys with him; one gold and the other silver. The monster will give you only one chance to open the lock using one of the keys. If the box doesn’t open, the monster will kill you. Since the monster is a bit helpful it would give you a clue in finding out the correct key. Can you choose the correct key by deciphering the below clue? A GKOY OEPD LYEO DCNO EAAR NNN

An old man lives alone in a flat. Because of his old age, he is not able to move comfortably and hence most of the things are delivered to his home. On Friday while delivering the mail, the postman felt something suspicious in the flat and tried to look inside through the key hole and he saw a blood filled body of the old man. The police arrived at the scene. On the outside of flat they found two bottles of warm milk, Tuesday newspaper, some unopened mails and some gifts. Who killed the old man and how did the police know who to arrest?

A man placed a $100 dollar bill on his desk and left for work. When he returned back the money was gone. He has three suspects: the cook, the maid and the electrician. The cook said he put the bill under a book on his desk to keep it safe. The man checked and it is no longer there. The maid said she moved the bill to the inside of the book between page 1 and 2 while she was cleaning. Again, the man checked the book and there was nothing between page 1 and 2. The electrician said he saw the bill sticking out of the book and he moved it between page 2 and 3 to keep it safe. Who stole the money?

A man placed a $100 dollar bill on his desk and left for work. When he returned back the money was gone. He has three suspects: the cook, the maid and the electrician. The cook said he put the bill under a book on his desk to keep it safe. The man checked and it is no longer there. The maid said she moved the bill to the inside of the book between page 1 and 2 while she was cleaning. Again, the man checked the book and there was nothing between page 1 and 2. The electrician said he saw the bill sticking out of the book and he moved it between page 2 and 3 to keep it safe. Who stole the money?

You have three boxes. One has only red marbles, one has only blue marbles and the third has an equal number of red and blue marbles. The labels on the boxes have intentionally been switched so that each box is now marked incorrectly. Your job is to relabel the boxes correctly. Of course you could just look in the boxes to find out which labels match, but can you do it without looking into each box? Reach into any one of the boxes and select one marble. Can you now correctly label all three boxes? If not, select a second marble from any box. What is the fewest number of marbles you need to inspect in order to correctly label each box?

One evening there was a murder in the home of married couple, their son and daughter. One of these four people murdered one of the others. One of the members of the family witnessed the crime. The other one helped the murderer. These are the things we know for sure: The witness and the one who helped the murderer were not of the same sex. The oldest person and the witness were not of the same sex. The youngest person and the victim were not of the same sex. The one who helped the murderer was older than the victim. The father was the oldest member of the family. The murderer was not the youngest member of the family. Who was the murderer?

A professor asked John to write down any multi-digit number. But, he put a condition, the number should not end with a zero. John put down the number 96452. Then the professor asked John to add up the five digits and subtract the total from the original number. John did and here is what he got: 96452 – 26 = 96426 The professor then asked John to cross out any one of the five digits and tell him the remaining numbers. John crossed out the 2 and told the professor the rest of the digits. John neither told the professor the original number nor what he had done with it. Yet, the professor told John the exact number he had crossed out. How is it possible?

A king decided to let a prisoner try to escape the prison with his life. The king placed 2 marbles in a jar that was glued to a table. One of the marbles was supposed to be black and one was supposed to be blue. If the prisoner picked the blue marble, he would escape the prison with his life. If he picked the black marble, he would be executed. However, the king was very mean and he wickedly placed 2 black marbles in the jars without any blue marbles. The prisoner witnessed the king only putting 2 black marbles in the jars. The jars were not see-through, the jars were glued to the table and the prisoner was mute so he could not say anything. How did he escape with his life?