You are given a set of scales and 12 marbles. The scales are of the old balance variety. That is, a small dish hangs from each end of a rod that is balanced in the middle. The device enables you to conclude either that the contents of the dishes weigh the same or that the dish that falls lower has heavier contents than the other. The 12 marbles appear to be identical. In fact, 11 of them are identical, and one is of different weight. Your task is to identify the unusual marble and discard it. You are allowed to use the scales three times if you wish, but no more. Note that the unusual marble may be heavier or lighter than the others. How can you identify it and determine whether it is heavy or light?
Hint: Think in terms of "groups" rather than individual marbles, and consider how you can use each weighing to gather information about multiple marbles at once.
Number the marbles from 1 to 12. For the first weighing put marbles 1,2,3 and 4 on one side and marbles 5,6,7 and 8 on the other. The marbles will either they balance or not. If they balance, then the different marble is in group 9,10,11,12. Thus, we would put 1 and 2 on one side and 9 and 10 on the other. If these balance then the different marble is either 11 or 12. Weigh marble 1 against 11. If they balance, the different marble is number 12. If they do not balance, then 11 is the different marble. If 1 and 2 vs 9 and 10 do not balance, then the different marble is either 9 or 10. Again, weigh 1 against 9. If they balance, the different marble is number 10, otherwise, it is number 9. That was the easy part. What if the first weighing 1,2,3,4 vs 5,6,7,8 does not balance? Then any one of these marbles could be a different marble. Now, in order to proceed, keep track of which side is heavy for each of the following weighings. Suppose that 5,6,7 and 8 is the heavy side. We now weigh 1,5 and 6 against 2,7 and 8. If they balance, then the different marble is either 3 or 4. Weigh 4 against 9, a known good marble. If they balance then the different marble is 3 or 4. Then, if 1,5 and 6 vs 2,7 and 8 do not balance, and 2,7,8 is the heavy side, then either 7 or 8 is a different, heavy marble, or 1 is a different, light marble. For the third weighing, weigh 7 against 8. Whichever side is heavy is the different marble. If they balance, then 1 is the different marble. Should the weighing of 1,5 and 6 vs 2,7 and 8 show 1,5,6 to be the heavy side, then either 5 or 6 is a different heavy marble or 2 is a light different marble. Weigh 5 against 6. The heavier one is the different marble. If they balance, then 2 is a different light marble.
You live in a one story house made entirely of redwood. What color would the stairs be?
A boy was at a carnival and went to a booth where a man said to the boy, "If I write your exact weight on this piece of paper then you have to give me $50, but if I cannot, I will pay you $50." The boy looked around and saw no scale so he agrees, thinking no matter what the carny writes he'll just say he weighs more or less. In the end the boy ended up paying the man $50. How did the man win the bet?
Mr. and Mrs. Mustard have six daughters and each daughter has one brother. How many people are in the Mustard family?
What has six faces, but does not wear makeup, has twenty-one eyes, but cannot see? "What is it?"
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How do you make the number 7 even without addition, subtraction, multiplication, or division?
There are 10 people in an empty, square room. Each person has full sight of the entire room and everyone in it without turning his head or body or moving in any way (other than the eyes). Where can you place an apple so that all but one person can see it?
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How can you take 2 from 5 and leave 4?
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When can you add two to eleven and get one as the correct answer?
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A pregnant lady named her children: Dominique, Regis, Michelle, Fawn, Sophie, and Lara. What will she name her next child? Jessica, Katie, Abby, or Tilly?
Romeo and Juliet are found dead on the floor in a bedroom. When they were discovered, there were pieces of glass and some water on the floor. The only furniture in the room is a shelf and a bed. The house is in a remote location, away from everything except for the nearby railroad track. What caused the death of Romeo and Juliet?
Three playing cards in a row. Can you name them with these clues? There is a two to the right of a king. A diamond will be found to the left of a spade. An ace is to the left of a heart. A heart is to the left of a spade. Now, identify all three cards.
I'm not clothes but I cover your body; The more I'm used, the thinner I grow. What am I?
A man was found dead next to a 13 story building. The police say it was a suicide, but you say it was a homicide (someone killed him). To prove this, you go to each floor on the building, open the window, and toss a penny out. You do this to each floor until you reach the 13th floor, open the window, and toss a penny out. How does this prove it wasn't a suicide?