Mathematical Puzzle

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 peopleâ€™s names(n+1), You can ask only one question from the people. Do you know this name ?
How many maximumÂ number of questions you need to ask to know the celebrity name?
Note: assume all names are unique. and you know the persons by name(but donâ€™t know if he is celebrity)
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There is a building of 100 floors Â If an egg drops from the Nth floor or above it will break.Â If itâ€™s dropped from any floor below, it will not break. Youâ€™re given 2 eggs. Find N, while minimizing the number of drops for the worst case.
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Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 18 MPH between the 2 friends until the friends meet.
How many miles does the pigeon travel?
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Below the four parts have been reorganized. The four partitions are exactly the same in both arrangements. Why is there a hole?
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Both triangles are made of identical parts. In the bottom one is one empty square though. How is it possible?
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A frog is at the bottom of a 30 meter well. Each day he summons enough energy for one 3 meter leap up the well. Exhausted, he then hangs there for the rest of the day. At night, while he is asleep, he slips 2 meters backwards. How many days does it take him to escape from the well?
Note: Assume after the first leap that his hind legs are exactly three meters up the well. His hind legs must clear the well for him to escape.
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There are twenty coins sitting on the table, ten are currently heads and tens are currently tails. You are sitting at the table with a blindfold and gloves on. You are able to feel where the coins are, but are unable to see or feel if they heads or tails. You must create two sets of coins. Each set must have the same number of heads and tails as the other group. You can only move or flip the coins, you are unable to determine their current state. How do you create two even groups of coins with the same number of heads and tails in each group?
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You have infinite supply of water. You also have 5 quart and 3 quart buckets. What is the least number of steps you will require to measure precisely 4 quarts?
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Two observations were made of a clock at different time:
1st observation:
The hour hand is exactly at a minute mark and the minute hand is six minutes ahead of it.2nd observation:
The hour hand is exactly on a dissimilar minute mark and the minute hand is seven minutes ahead of it.Can you find out how much time has passed between the above two observations?
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