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 process of elimination and divide the marbles into groups strategically for each weighing. The key is to maximize the information you can gain from each weighing.
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.
I am something people love or hate. I change people's appearances and thoughts. If a person takes care of them self I will go up even higher. To some people, I will fool them. To others, I am a mystery. Some people might want to try and hide me but I will show. No matter how hard people try I will Never go down. What am I?
Only one color, but not one size, Stuck at the bottom, yet easily flies. Present in sun, but not in rain, Doing no harm, and feeling no pain. What is it?
Who is that with a neck and no head, two arms and no hands? What is it?
If eleven plus two equals one, what does nine plus five equal?
How can you write down eight eights so that they add up to one thousand?
It can't be seen, can't be felt, can't be heard, and can't be smelt. It lies behind stars and under hills, And empty holes it fills. It comes first and follows after, Ends life, and kills laughter. What is it?
What English word retains the same pronunciation, even after you take away four of its five letters?
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.
What is it that given one, you'll have either two or none?
George, Helen, and Steve are drinking coffee. Bert, Karen, and Dave are drinking soda. Using logic, is Elizabeth drinking coffee or soda?
When John was six years old he hammered a nail into his favorite tree to mark his height. Ten years later at age sixteen, John returned to see how much higher the nail was. If the tree grew by five centimeters each year, how much higher would the nail be?
I am four times as old as my daughter. In 20 years time I shall be twice as old as her. How old are we now?
Which of the following words don't belong in the group and why? CORSET, COSTER, SECTOR, ESCORT, COURTS
Lily is a lilypad in a small pond. Lilly doubles her size each day, On the 20th day she covers the whole pond. On what day was Lily half the size of the pond?
What common English verb becomes its own past tense by rearranging its letters?
The ages of a father and son add up to 66. The father's age is the son's age reversed. How old could they be? (3 possible solutions).
There was a man who was born before his father, killed his mother, and married his sister. Yet, there was nothing wrong with what he had done. Why?
There are two sisters; one gives birth to the other, who in turn gives birth to the first. Who are they?
What two whole, positive numbers have a one-digit answer when multiplied and a two-digit answer when added?
Which word is the odd one out: Seventy, Brawl, Clover, Proper, Carrot, Swing, Change, Travel, Sacred, Stone?