Luck of the Draw

Job interviews can be a total crapshoot. Just be glad you did't get asked these kinds of questions...or maybe you did. I compiled a short list of twelve brain teasers representative of what my friends and I have been asked in the past month or two during job interviews. An average interview may contain 3-5 such questions. At one company I took two, 30-minute tests filled with these kinds of questions. At another, my interviewer asked me arithmetic questions for 25 minutes. Six of these questions I was asked in real job interviews while the others were asked of my friends. Oh yeah, you only get pen and paper for the last three questions. Solutions are listed in the comments. Enjoy. (number 8 is my favorite)

1) Casino Game
A casino wants to try out a new game. The 'dealer' will blindly draw a poker chip out of a hat that contains 100 chips, each numbered from $1-$100. Each number occurs only once. Before the dealer draws the number, the player makes a guess. If his guess is within 10 above, or 10 below the number drawn, then he wins the dollar amount on the chip. In order to make a profit (on average) What is the minimum amount that the casino should charge players to play this game?

2) The Five Pirates
There are 5 pirates and 100 gold coins. In turn, each will propose a plan how to divide the 100 coins amongst themselves. After each proposal they will all vote on whether or not to accept the proposal. A proposal needs a majority vote (more than 50%) to pass. If it is not passed, the proposer has to leave. The process is repeated until a consensus is reached. (Obviously, if only 1 pirate remains after 4 rounds of voting then he gets all of the coins.) If each pirate wants to get as many coins as possible, how many will each pirate get?

3) Digital Option
You are a trader at an investment bank selling a digital option. Upon sale of the option, you agree to pay the buyer $1 in the event that company A's stock's price reaches $100. If company A's stock is currently worth $75, at what price should you sell the digital option?

4) A Wise King
A king over 10 provinces requires each province pay 1,000 gold coins, each weighing 10 oz., in taxes each year. This year, the king has been told that one of the provinces cheated him, by shaving 1 oz. of gold from each coin. How can the king prove which province has cheated him using only one measurement on a scale?

5) Missing Number
At the end of the day your boss is going to give you a spreadsheet. The spreadsheet will contain 9,999 numbers that are out of order. Each number is a distinct integer falling from 1 to 10,000. What will be the fastest way to tell which number is missing? i.e. the shortest amount of time for a computer. (hint: sorting the list is too slow)

6) Area of a Parallelogram
A parallelogram is divided into 4 triangles by drawing 2 lines, one from each vertex to it's opposite vertex. What is the area of the parallelogram in terms of the area of one of the triangles?

7) Integers
There are three integers, x,y, and z. They all add up to 20. x must be bigger than 0, y must be bigger than 4, and z must be bigger than 5. A solution is a set of x,y, and z that meet all the criterion. How many solutions are there?

8) One Hundred Story Building
You have two identical dinner plates and you are curious to find out how durable they are. You are in a 100 story building and decide to drop them out of the window on each floor until you know the height that produces a shattered plate when dropped. Minimizing the number of drops (on average), how do you determine the exact height (within one story) at which the plates break when dropped? (If you start at the first floor and drop on every floor until one breaks, you would know the exact height. Since you have two plates, you should use this to your advantage)

9-11) Arithmetic
What's 798*8 ?

Tell me the square root of 200 within 2 decimal places?

You have a roulette wheel, a deck of cards, and a six-sided die. What is the probability that they all turn up on the same number?

12) Logic Puzzle
The following 4 statements are written on a note card, how many of them are true?

Exactly 1 statement on this card is false
Exactly 2 statements on this card are false
Exactly 3 statements on this card are false
Exactly 4 statements on this card are false