Difficulty Popularity

Determine the value of the following series

1/(7^1) + 2/(7^2) + 1/(7^3) +2/(7^4) + 1/(7^5) + ....

1/(7^1) + 2/(7^2) + 1/(7^3) +2/(7^4) + 1/(7^5) + ....

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In a bowl, there are several chits with distinct numbers on them. You have to choose any two of them at random.

Will you accept the 2 to 1 bet that the numbers will be relatively prime will you accept it?

For instance:

If the numbers you pick are 6 and 13, you lose $1.

If the numbers you pick are 5 and 25, you win $2.
**category** :
LOGIC

Will you accept the 2 to 1 bet that the numbers will be relatively prime will you accept it?

For instance:

If the numbers you pick are 6 and 13, you lose $1.

If the numbers you pick are 5 and 25, you win $2.

Difficulty Popularity

A thief was running from the police after the biggest theft the town saw. He took his guard in one of the thirteen caves arranged in a circle. Each day, the thief moves either to the adjacent cave or stay in the same cave. Two cops goes there daily and have enough time to enter any two of the caves out of them.

How will the cop make sure to catch the thief in minimum number of days and what are the minimum number of days?
**category** :
LOGIC

How will the cop make sure to catch the thief in minimum number of days and what are the minimum number of days?

Difficulty Popularity

We all know that New Year occurs after a week from Christmas and thus it falls on the same day as of Christmas. But this will not happen in 2050. In 2050, Christmas will appear on Sunday while New Year will appear on Saturday.

How can this be possible ?

How can this be possible ?

Difficulty Popularity

A wicked sorcerer felt enmity towards elf and thus he chooses four among the rest of the elf's and concealed them. The elves are concealed in the ground in a manner that apart from their head the rest of their body was underneath the ground. The elf's are unable to move their body and can only see in that direction that they are facing. All the elf's are concealed underground in such a way that they form a straight line and among those four elf's that are concealed underground one of the elf is detached form the other three elf's via wall. The entire elf's are in the same direction. The elf that is the furthest can only see the heads of its friends in front and a wall. The elf that is second last can only see one head of his friend and a wall. The second elf can only view the wall. The elf can see nothing.

The sorcerer understands the situation and tells the elf's that he has placed hats over their heads. Among the hats places two hat are blue and the other two are red. Among all the four elfs one of the elf has to guess that which colour hat is he wearing. If the elf answers correctly then he shall be set free or else he will have to dig beneath the ground till the very last.
**category** :
LOGIC

The sorcerer understands the situation and tells the elf's that he has placed hats over their heads. Among the hats places two hat are blue and the other two are red. Among all the four elfs one of the elf has to guess that which colour hat is he wearing. If the elf answers correctly then he shall be set free or else he will have to dig beneath the ground till the very last.

Difficulty Popularity

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 a 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. You are asked to both identify it and determine whether it is heavy or light.
**category** :
LOGIC

The 12 marbles appear to be identical. In fact, 11 of them are identical, and one is of a 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. You are asked to both identify it and determine whether it is heavy or light.

Difficulty Popularity

The world is facing a serious viral infection. The government of various countries have issued every citizen two bottles. You as well have been given the same. Now one pill from each bottle is to be taken every day for a month to become immune to the virus. The problem is that if you take just one, or if you take two from the same bottle, you will die a painful death.

While using it, you hurriedly open the bottles and pour the tablets in your hand. Three tablets come down in your hand and you realize they look exactly the same and have same characteristics. You can’t throw away the pill as they are limited and you can’t put them back or you may put it wrong and may die someday.

How will you ensure that you are taking the right pill?
**category** :
LOGIC

While using it, you hurriedly open the bottles and pour the tablets in your hand. Three tablets come down in your hand and you realize they look exactly the same and have same characteristics. You can’t throw away the pill as they are limited and you can’t put them back or you may put it wrong and may die someday.

How will you ensure that you are taking the right pill?

Difficulty Popularity

You need to divide 50 marbles(25-red and 25-blue) into two boxes such that the probability of picking red marble is maximized.

Following conditions need to hold true :

1. None of box is empty

2. All the marbles must be in one of two boxes.
**category** :
LOGIC

Following conditions need to hold true :

1. None of box is empty

2. All the marbles must be in one of two boxes.

Difficulty Popularity

Four people need to cross a dark river at night.

* They have only one torch and the river is too risky to cross without the torch.

* If all people cross simultaneously then torch light wont be sufficient.

* Speed of each person of crossing the river is different.cross time for each person is 1 min, 2 minutes, 7 minutes and 10 minutes.

What is the shortest time needed for all four of them to cross the river ?

* They have only one torch and the river is too risky to cross without the torch.

* If all people cross simultaneously then torch light wont be sufficient.

* Speed of each person of crossing the river is different.cross time for each person is 1 min, 2 minutes, 7 minutes and 10 minutes.

What is the shortest time needed for all four of them to cross the river ?

Difficulty Popularity

You are trapped with a lion in a cage with 1 unit as its radius. Both you and the lion can run effortlessly at the speed of one unit.

1) The lion is quite hungry and all he wants is to catch you and eat you up. Will he be able to do that?

2) If yes, how long do you have till he does that?
**category** :
LOGIC

1) The lion is quite hungry and all he wants is to catch you and eat you up. Will he be able to do that?

2) If yes, how long do you have till he does that?

Difficulty Popularity

In a recreational activity, you are given four different jars of 2 liters, 4 liters, 6 liters and 8 liters respectively with an unlimited water supply. Then you are asked to measure exactly 5 liters of water using them.

How will you do it?

How will you do it?

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