Determine winner of 2/9 number game

Two players play the following game: they pick a random number N (less than 2 billion) then, 
starting from 1, take turns multiplying the number from the previous turn with either 2 or 9 (their choice). Whoever reaches N first wins. 
The candidate should write a function that given N decides who wins (first or second player)?

Given n coins for two players playing a game. Each player can pick at least 1 and at most 5 coins in one turn. The player who picks the last coin loses the game. If they play optimally, which player will win the game?

What strategy should be used to kill the fewest dwarfs, and what is the minimum number of dwarfs that can be saved with this strategy?

A dwarf-killing giant lines up 10 dwarfs from shortest to tallest. Each dwarf can see all the shortest dwarfs in front of him, but cannot see the dwarfs behind himself. The giant randomly puts a white or black hat on each dwarf. No dwarf can see their own hat. The giant tells all the dwarfs that he will ask each dwarf, starting with the tallest, for the color of his hat. If the dwarf answers incorrectly, the giant will kill the dwarf. Each dwarf can hear the previous answers, but cannot hear when a dwarf is killed. What strategy should be used to kill the fewest dwarfs, and what is the minimum number of dwarfs that can be saved with this strategy?

Source: http://www.businessinsider.com/toughest-job-interview-questions-2013-7?op=1#ixzz2a9upxPNJ

"We're playing a game. Cards numbered from 1-10 are placed in a hat. whatever card is drawn is the paid out amount. how much should i charge you to play this game? If you can redraw by placing the first card back into the hat, what is the new price?"

You wake up groggily in the dark, On the wall next to you is a switch. what you will do ?

How many passes does it take to fill in slots so that max number of people are happy

 There are 5 slots(1,2,3,4,5) and 5 people(A,B,C,D,E). Each of them provide their preferences. A=1, B=2, C=3, D=4, C=4. Given an arbitary starting sequence say BCDEA, going clock wise: how many passes does it take to fill in those slots so that max number of people are happy. People are happy if A gets 1, B gets 2, C gets 3, etc. Remember D and E cannot be kept happy together at the same time because both of them prefer Slot-4.

So Question is : Can you do better than N passes?

Suppose you reach your home and noticed that the light bulb in your corridor is not working. What will you do in such a situation?