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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.

Following conditions need to hold true :

1. None of box is empty

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

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You have a pair of unbiased dices. You throw them together till you get a sum of 4 or 7.

What is the probability that you get a sum of 4 before the sum of 7?

What is the probability that you get a sum of 4 before the sum of 7?

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I have two hourglasses

A) Measures an exact 7 hours

B) Measures an exact 4 hours.

Using these two hour glasses, you need to measure an exact nine hours ?

A) Measures an exact 7 hours

B) Measures an exact 4 hours.

Using these two hour glasses, you need to measure an exact nine hours ?

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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.

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.

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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 ?

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I have two rectangular bars.

They have property such that when you light the fire from one end , it will take exactly 60 seconds to get completely burn.

However they do not burn at consistent speed (i.e it might be possible that 40 percent burn in 55 seconds and next 60 percent can burn in 10 seconds).

Problem is : How do you measure 45 seconds ?

They have property such that when you light the fire from one end , it will take exactly 60 seconds to get completely burn.

However they do not burn at consistent speed (i.e it might be possible that 40 percent burn in 55 seconds and next 60 percent can burn in 10 seconds).

Problem is : How do you measure 45 seconds ?

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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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