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Argus Interview Puzzle #1 - Hard Probability Question

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Imagine a situation in your mind. You are playing a coin game with your friend where you have pre-decided the sequence that you require. The coin is fair and you both keep tossing it till you get the desired sequence.

The predefined sequence for you is H T H.
The predefined sequence for your friend is H T T.

You keep tossing the coin and writing it down till you get the required sequence. You play several games and at the end, the one with the average score less will win.

Game 1 result:
You: H T T H T H
Your score: 6
Your friend: H T H H H T H H T T
Your friends' score: 10

Game 2 result:
You: T T H T T H H T H
Your score: 9
Your friend: T T H H T H T T
Your friends' score: 8

Game 3 result:
You: T T H H T H
Your score: 6
Your friend: H H T H T T
Your friends' score: 6

Now, after playing 3 games, your score is 7 (average) and your friend's score is 8 (average). Assume that you keep playing like this for several many games, what of the following outcomes are you expecting at the end?
a) Your average score is lower and you win.
b) Your friend's average score is lower and he wins.
c) Both have equal scores and the match ties.

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Argus Interview Puzzle #2 - Famous Elevator Riddle

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Tanu lives on the 13th floor takes the elevator down to the ground floor every morning and goes to her office.

In the evening, when she comes back on a rainy day , or if there are other people around in the elevator, she goes to her 13th floor directly. Otherwise, she goes to the 1oth floor and walks up three flights of stairs to his apartment.

Whats the reason for her unusual behavior ?

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Argus Interview Puzzle #3 - Karamchand Detective Mystery Cipher Riddle

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Karamchand , A well known consulting detective is currently working on an international case where oil is illegally sold.

While inspecting he finds a note under a shelf : 710 57735 34 5508 51 7718

Currently there are 3 suspects: Rooney Bill and Owen.

He breaks the code and found the suspect. can you ?

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Argus Interview Puzzle #4 - 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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Argus Interview Puzzle #5 - Conditional Probability Brain Teaser

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The students of a particular class were given two tests for evaluation. Twenty Five percent of the class cleared both the tests and forty five percent of the students were able to clear the first test.

You have to calculate the percentage of those students who passed the first test and were also able to pass the second test. How will you do it?

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