- There is a hallway with 100 lockers, numbered sequentially from 1 to 100. The lockers have two possible states, open and closed. Initially all the lockers are closed. The first kid who walks down the hallway flips every locker to the opposite state, that is, opens them all. The second kid flips the second locker door and every other locker door to the opposite state, that is, closes them. The third kid flips every third door, opening some that are closed, and closing others, which were open. The fourth kid does every fourth door, etc. After 100 kids have passed down the hallway, how many lockers are open?
- If a rook and a bishop of a standard chess set are randomly placed on a chessboard, what is the probability that one is attacking the other? (Note that both are different colored pieces.)
- At University of Probability, there are 375 freshmen, 293 sophomores, 187 juniors, & 126 seniors. One student will randomly be chosen to receive an award. What percent chance is there that it will be a junior? Round to the nearest whole percent.
- A blindfolded man is asked to sit in the front of a carom board. The holes of the board are shut with lids in random order, i.e. any number of all the four holes can be shut or open.
Now the man is supposed to touch any two holes at a time and can do the following.
- Open the closed hole.
- Close the open hole.
- Let the hole be as it is.
After he has done it, the carom board is rotated and again brought to some position. The man is again not aware of what are the holes, which are open or closed. How much minimum number of turns does the blindfolded man require to either open all the holes or close all the holes? (Note that whenever all the holes are either open or close, there will be an alarm so that the blindfolded man will know that he has won.)
- Doo-Bee-Doo had born on 1468 B.C. He had lived one-fourth of his life as a boy, one-third of his life as a youth, one-fifth of his life as a man and the remaining 52 years as an old man. Which year did Doo-Bee-Doo die?
- You can construct a number from any date of the year by adding the number of the month to the number of the day. For example: May 15th would become the number 20, since May is the fifth month, and 5 + 15 = 20. November 14 would become 25, and so on... How many different numbers can you make, using dates of the Gregorian calendar?
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Everyday in his business a merchant had to weigh amounts from 1 kg to 121 kgs, to the nearest kg. What is the minimum number of different weights required and how heavy should they be?
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A group of friends went on a holiday to a hill station. It rained for 13 days. But when it rained in the morning, the afternoon was lovely. And when it rained in the afternoon, the day was preceded by clear morning. Altogether there were 11 very nice mornings and 12 very nice afternoons. How many days did their holiday last?
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