Infosys Interview Puzzles

On a circle there are 2014 light bulbs, 2 are ON, and 2012 are OFF. You can choose any bulb and change the neighbor’s state from ON to OFF or from OFF to ON. Doing so, can we get all 2014 light bulbs on ? If yes, How?
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A Bear has fallen from a height of 10m from ground. It reached ground in sqrt(2) seconds. Luckily it didn’t get hurt.
What is the color of that Bear? Prove it scientifically.
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100 people standing in a circle in an order 1 to 100. No.1 has a sword. He kills next person (i.e. no. 2) and gives sword to next to next (i.e no.3). All person does the same until only 1 survives. Which number survives at the last?
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There are (n+1) people in a party, they might or might not know each others names.
There is one celebrity in the group(total n +1 people), celebrity does not know any of n peoples by name and all n people know celebrity by name.
You are given the list of people’s names(n+1), You can ask only one question from the people. Do you know this name ?
How many maximum number of questions you need to ask to know the celebrity name?
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You are trying to cook an egg for exactly fifteen minutes, but instead of a timer, you are given two ropes which burn for exactly 1 hour each. The ropes,are of equal densities. How can you cook the egg for exactly fifteen minutes?
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You have two jars, 50 red marbles and 50 blue marbles. You need to place all the marbles into the jars such that when you blindly pick one marble out of one jar, you maximize the chances that it will be red. When picking, you’ll first randomly pick a jar, and then randomly pick a marble out of that jar. You can arrange the marbles however you like, but each marble must be in a jar.
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