Which number survives at the last?

100 people are standing in a circle in an order 1 to 100 and 100 adjacent to 1. No.1 has a sword. He kills the next person (i.e. no. 2) and gives the sword to the next (i.e  no.3). This continues until only one person remains. Which number survives at the last? Can you generalize your solution to N people? Hint: First solve the problem for powers of 2.

Birthday on a Sunday!!

It seems to me that people do not value how often their birthday falls on a Sunday, or for that matter a weekend - when many friends and relatives get a chance to wish them. So supposing your birthday falls on a Sunday this year, value it and count the number of years you need to wait until your birthday falls on a Sunday again. Do let me know your answers. Mind it, the wait can be long, but it is so worth it.

Now that you would have thought about this problem in your head, here's something that will make you grab a sheet of paper and a pen. If your birthday falls on a weekend, how long should you wait for a birthday on a weekend again? Do post your answer, for this is bound to get interesting!! Count the number of birthdays in a lifetime :)

Fair experiment with unfair coin!

The puzzle is simple to state: You are given a biased coin with 60% chance for getting heads and 40% chance of getting tails while tossing. Design an experiment with two equally likely outcomes using the coin.

Think out of the box!

2 rooms, 1 light bulb in one room and the other room has 3 switches out of which only one of the light bulb switches on/off. The rooms are not viewable from each other. You as a single person has just one chance to find which switch operates the bulb. How can this be done?

An Interval Graph

Six professors had been to the library on the day when the rare tractate was stolen. Each had entered once, stayed for some time and then left. If two were in the library at the same time, then at least one of them saw the other. Detectives questioned the professors and gathered the following testimony:


A said he saw B and E
B reported he saw A and I
C claimed he saw D and I
D said he saw A and I
E testified to seeing B and C
I said that she saw C and E

One of the professors lied. Who was it?