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Bloomberg LP Interview Puzzle #1 - Coin Probability Brain Teasers

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You keep tossing a fair coin for twenty times. Each time, the coin lands up with tails up.

What is the probability that if you toss it now, the coin will land with heads up this time?

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Bloomberg LP Interview Puzzle #2 - Popular Interview Problem

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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 ?

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Bloomberg LP Interview Puzzle #3 - River Crossing Problem

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A guard is positioned at the one side of bridge say 'A'.
* His task is to shoot all those who try to leave from 'A' to other side say 'B'.
* He also need to welcome the person who come from other side 'B' to his side 'A'.

The guard comes out of his post every 1 hour and looks down the bridge for any people trying to leave.
Monica a brilliant girl is at side 'A' and wish to go to other side 'B'. She also know's it would take her 1:45 hr to cross the river.

She comes with an super idea and able to cross the river.How did Monica cross the river ?

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Bloomberg LP Interview Puzzle #4 - Fake Coin Brain Teaser

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In front of you, there are 9 coins. They all look absolutely identical, but one of the coins is fake. However, you know that the fake coin is lighter than the rest, and in front of you is a balance scale. What is the least number of weightings you can use to find the counterfeit coin?

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Bloomberg LP Interview Puzzle #5 - Cake Grandma bridge Logic Problem

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Rohit is on his way to visit your Grandma, who lives at the end of the state.It's her birthday, and he want to give her the cakes that he has made.Between his place and her grandma house, he need to cross 7 toll bridges.
Before you can cross the toll bridge, you need to give them half of the cakes you are carrying, but as they are kind trolls, they each give you back a single cake.

How many cakes do rohit have to carry with him so he can reach his grandma home with exactly 2 cakes?

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