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 sets and subsets, and consider how you can cleverly divide the 12 marbles into groups to maximize the information you can gather 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.
You walk up to a mountain that has two paths. One leads to the other side of the mountain, and the other will get you lost forever. Two twins know the path that leads to the other side. You can ask them only one question. Except! One lies and one tells the truth, and you don't know which is which. So, What do you ask?
What weighs more, a pound of feathers or a pound of stones?
A logician with some time to kill in a small town decided to get a haircut. The town had only two barbers, each with his own shop. The logician glanced into one shop and saw that it was extremely untidy. The barber needed a shave, his clothes were unkempt, and his hair was badly cut. The other shop was extremely neat. The barber was freshly shaved and spotlessly dressed, his hair neatly trimmed. Why did the logician return to the first shop for his haircut?
George, Helen, and Steve are drinking coffee. Bert, Karen, and Dave are drinking soda. Using logic, is Elizabeth drinking coffee or soda?
Little Tommy Tittletat took two Ts, to tie two ups to two tall trees, to torment the terrible little tat. How many T's in all of that?
A man went on a trip with a fox, a goose, and a sack of corn. He came upon a stream that he had to cross and found a tiny boat to use to cross the stream. He could only take himself and one other - the fox, the goose, or the corn - one at a time. He could not leave the fox alone with the goose or the goose with the corn. How does he get all safely over the stream?
81 x 9 = 801. What must you do to make the this equation true?
One of the four words does not belong with the other three. Which word does not belong? What is it that the others have in common? 1. Green, yellow, red, blue. 2. April, December, November, June. 3. Cirrus, calculus, cumulus, stratus. 4. Carrots, radishes, potatoes, cabbages. 5. Fork, comb, rake, shovel.
If you have two coins which total 35 cents and one of the coins is not a dime, what are the two coins?
Open me, and you can't see me without a mirror. Close me and you can't see me at all. What am I?
I am a 5-letter word. Take away the first letter and I am a place's name. Take away the first two letters and I become the opposite of the 5 letter word. What am I?
You buy me taken apart, To redo what has been undone; Four of my pieces have one sharp corner, The rest of them have none. What am I?
What only works the first time you use it?
Which side of the turkey has the most feathers?
It's raining, and you pass a bus stop. There are three people there; your trustworthy friend, the love of your life, and a woman about to go into labor. Your smart car only has two seats. What do you do?
What's the least number of chairs you would need around a table to sit four fathers, two grandfathers, and four sons?
What's 3/7 chicken, 2/3 cat, and 2/4 goat?
I can hold you prisoner Or set you free I can swing with ease (Though not from a tree) I have many shapes I have many sizes Yet, 'til we shake hands I'll hide my surprises. What am I?
Many years ago, a wealthy old man was near death. He wished to leave his fortune to one of his three children. The old man wanted to know that his fortune would be in wise hands. He stipulated that his estate would be left to the child who would sing him half as many songs as days that he had left to live. The eldest son said he couldn't comply because he didn't know how many days his father had left to live, and besides he was too busy. The youngest son said the same thing. The man ended up leaving his money to his third child, a daughter. What did his daughter do?
If you see me, I see you. If you move, then I'll move too. When you touch me, I touch you. I do everything you do except for one thing. No matter how hard I try, I can never speak. What am I?