These are just some Logic Problems.
1. A ship is at anchor. Over the side of the ship is a rope ladder 6 feet in height, with rungs 1 foot apart, reaching down to the water level. The tide is rolling in at the rate of 1 foot per hour. In how many hours will the tide overflow the ship?
2. A snail is at the bottom of a 30 foot well. During the daytime, the snail crawls up 3 feet, but at night, it slides down 2 feet. In how many days will the snail be able to reach the top of the well and escape?
3. Four men are at one end of a bridge that they must all cross in no more than 17 minutes. The bridge can accommodate at most two men crossing at the same time. It is night time, and to cross the bridge, they must cross using the one flashlight that they share. The must walk the flashlight back and forth on the bridge; they cannot throw the flashlight.The men walk at different speeds - One can cross the bridge in one minute, Two can cross in two minutes, Five crosses in five minutes, and Ten crosses in ten minutes. When two of the men cross together, they can only go at the speed of the slower man.
For example, if Two and Five cross together, and Two returns with the flashlight, the total round trip time is 5 + 2 minutes, and Five would be at the other side, but since Two had to return with the flashlight, he would be back at the originating side. Any man can cross any number of times, but the one flashlight must be used on all crossings. How can all four men get across the bridge in no more than 17 minutes total?
4. There are three boxes of fruits, with one box containing only apples, the second box containing only oranges, and the third box containing apples and oranges. The boxes are labeled APPLES, ORANGES, and APPLES/ORANGES. You know that the label currently on each box has been labeled incorrectly. Without being allowed to look inside the boxes, and if you are allowed to pick only one fruit from any box of your own choosing, by knowing the whether the one fruit you pick is apple or orange, are you able to move the labels and correctly label the boxes as to the fruits that the boxes contain?
5. What is the next letter in the sequence? OTTFFSS_ ?
6. What is unusual about the following sentence? " I MAIM NINE MEN IN MIAMI "
7. You are in jail guarded by two jailers, one of whom always tells the truth, and the other always lies. You do not know who tells the truth and who is the liar. There are two exit doors; one leads to freedom, and the other is a return to jail. You do not know which door leads to freedom, and which is a return to jail, but the jailers know which is which. You win a lottery and are allowed one chance to gain your freedom; which is, you may ask one question to either jailer of your choice, and to exit either door of your choice. It's up to you whether or not you decide to use the answer the jailer gives you to the question that you pose to him.
What question would you ask to which jailer, and how would you select which door to exit? The jailer must give you some answer. There is a way to ensure that you exit the freedom door.
(Note: This problem no. 7 was contributed by an old friend, Mr. D. Jones of Arizona, USA. We've known each other for over 40 years, first in Japan, and now in the US.)
8. If someone offered you a bet, that in a room of 50 people, at least two people (out of the 50) would have the same birthday, i.e. the month and date of the month, but not counting the year of birth, which side of the bet would you take? That there would be two people with the same birthday, or that there would be no two people with the same birthday (month and date of the month)? Consider that there are only 50 people, but 365 days in a year - what is the chance that two people would have the same birthday?
(Note: This problem was one that I had encountered before and had thought of including, but an old friend, Mr. D. Bergt of Texas, USA, had recently suggested that it be included in this group of problems. Mr. Bergt is a friend of 40 years, and is also a friend of Mr. Jones, mentioned above.)
9. There are two rooms, not visible to each other. In one room are three lights, and in the other room are the three switches to turn on/off the lights, one switch per each light. You may enter and exit each room just once, and you may turn on/off each switch just once; though you don't have to enter/exit either room or switch on/off any light, if you don't wish. How can you determine which switch goes with which light? Assume that each light and switch operates normally and correctly - i.e. no malfunction.
10. There are two ropes, which are of different thickness and length. However, burned from one end, each rope will burn completely in exactly one hour. The rate at which the ropes burn is random, and not even. You do not have a clock or watch, but you do have sufficient matches to light the ropes. How are you able to measure out exactly 45 minutes of time using only the two ropes and matches?
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