# All Puzzles

• One theft happens in a village and police inspector asked one constable to reach the spot and take the FIR.
Due to night and too far from the station, constables didn’t go there and made a fake FIR. After reading the report the inspector suspended the constable for making a fake report with out reaching the spot.

How the inspector find that it is fake and they didn’t reach the spot ?

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• This is a popular probability puzzle in which you have to select the correct answer at random from the four options below.

Can you tell, whats the probability of choosing correct answer in this random manner.

1) 1/4
2) 1/2
3) 1
4) 1/4

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• Mr Albert go to his office by metro.
However nearby metro station is quite far from his place and he used to drive his bike to metro station daily with an average speed of 60km/hr. One day at halfway point he relized that due to heavy traffic he got late having average speed of just 30km/hr.

How fast he must drive for the rest of the way to catch the metro train ?

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• Also known as Hempel’s Paradox, for the German logician who proposed it in the mid-1940s, the Raven Paradox begins with the apparently straightforward and entirely true statement that “all ravens are black.”

The paradox here is that Hempel has apparently proved that seeing an apple provides us with evidence, no matter how unrelated it may seem, that ravens are black. It’s the equivalent of saying that you live in New York is evidence that you don’t live in L.A., or that saying you are 30 years old is evidence that you are not 29. Just how much information can one statement actually imply anyway?

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• Imagine that a farmer has a sack containing 100 lbs of potatoes. The potatoes, he discovers, are comprised of 99% water and 1% solids, so he leaves them in the heat of the sun for a day to let the amount of water in them reduce to 98%. But when he returns to them the day after, he finds his 100 lb sack now weighs just 50 lbs. How can this be true? Well, if 99% of 100 lbs of potatoes is water then the water must weigh 99 lbs. The 1% of solids must ultimately weigh just 1 lb, giving a ratio of solids to liquids of 1:99. But if the potatoes are allowed to dehydrate to 98% water, the solids must now account for 2% of the weight—a ratio of 2:98, or 1:49—even though the solids must still only weigh 1lb. The water, ultimately, must now weigh 49lb, giving a total weight of 50lbs despite just a 1% reduction in water content. Or must it?

Although not a true paradox in the strictest sense, the counterintuitive Potato Paradox is a famous example of what is known as a veridical paradox, in which a basic theory is taken to a logical but apparently absurd conclusion.

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• In his final written work, Discourses and Mathematical Demonstrations Relating to Two New Sciences (1638), the legendary Italian polymath Galileo Galilei proposed a mathematical paradox based on the relationships between different sets of numbers. On the one hand, he proposed, there are square numbers—like 1, 4, 9, 16, 25, 36, and so on. On the other, there are those numbers that are not squares—like 2, 3, 5, 6, 7, 8, 10, and so on. Put these two groups together, and surely there have to be more numbers in general than there are justsquare numbers—or, to put it another way, the total number of square numbers must be less than the total number of square and non-square numbers together. However, because every positive number has to have a corresponding square and every square number has to have a positive number as its square root, there cannot possibly be more of one than the other.

Confused? You’re not the only one. In his discussion of his paradox, Galileo was left with no alternative than to conclude that numerical concepts like more, less, or fewer can only be applied to finite sets of numbers, and as there are an infinite number of square and non-square numbers, these concepts simply cannot be used in this context.

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• Imagine a fletcher (i.e. an arrow-maker) has fired one of his arrows into the air. For the arrow to be considered to be moving, it has to be continually repositioning itself from the place where it is now to any place where it currently isn’t. The Fletcher’s Paradox, however, states that throughout its trajectory the arrow is actually not moving at all. At any given instant of no real duration (in other words, a snapshot in time) during its flight, the arrow cannot move to somewhere it isn’t because there isn’t time for it to do so. And it can’t move to where it is now, because it’s already there. So, for that instant in time, the arrow must be stationary. But because all time is comprised entirely of instants—in every one of which the arrow must also be stationary—then the arrow must in fact be stationary the entire time. Except, of course, it isn’t.

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• John Farmer woke up one morning to pandemonium in his barnyard. The gate had been left open and the animals had wandered out during the night. When he looked out the window, he could see the chickens and the sheep. By the time he got downstairs he could see the goats, too. But he had to hunt for the cows and the horses. After an hour of running around, Jake finally got all his animals back in their pens. Using the clues below, determine how many of each animal the farmer had to find, what kind of mischief each type of animal got into, and how long it took the farmer to return each group of animals to their pens.

1. The animals running loose on the neighbor’s lawn were not the goats.
2. The twelve chickens, who were not eating Jake’s vegetable garden, took the most time to return to their pen.
3. Jake had five of one type of animal; he had an even number of all the other animals.
4. The animals he had the least number of were the ones found in the grain room. The animals he had the most of took him twenty minutes to catch.
5. The animals Jake had only two of took five minutes to catch while the animals he had six of took twice as long to catch.
6. Jake had six more chickens than goats but two more goats than sheep.
7. It took five minutes more to catch the horses than it took to catch the animals in the hay field but getting the horses took five minutes less than collecting the animals scattered around the barnyard.
8. It took Jake the same amount of time to collect the four animals in the hay field as it did to collect the goats.
 ANIMAL Number of animals Animals’ location time CHICKENS COWS GOATS x HORSES SHEEP x
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• Imagine that you’re about to set off walking down a street. To reach the other end, you’d first have to walk half way there. And to walk half way there, you’d first have to walk a quarter of the way there. And to walk a quarter of the way there, you’d first have to walk an eighth of the way there. And before that a sixteenth of the way there, and then a thirty-second of the way there, a sixty-fourth of the way there, and so on.

Ultimately, in order to perform even the simplest of tasks like walking down a street, you’d have to perform an infinite number of smaller tasks—something that, by definition, is utterly impossible. Not only that, but no matter how small the first part of the journey is said to be, it can always be halved to create another task; the only way in which it cannot be halved would be to consider the first part of the journey to be of absolutely no distance whatsoever, and in order to complete the task of moving no distance whatsoever, you can’t even start your journey in the first place.

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