## Some Logic Puzzles

**COIN PROBLEM:** *(hard!)*

There is a game where a coin gets tossed. If it comes up heads, you gain a

dollar. If it comes up tails, you lose half your money. You start with $0 (and

you can have fractional amounts of money, not limited to cents or anything,

money is just a real number).

After N tosses how many different possible values of money can you have?

Example:

toss heads: 1.0

toss tails: 0.5

toss tails: 0.25

toss heads: 1.25

toss heads: 2.25

When N=5, one possible value is 2.25

It may be trivial to write a program to simulate the coin tosses and discover

the function. But why is it what it is?

**DICE PROBLEM:**

Sue and Bob take turns rolling a 6-sided die. Once either person rolls a 6 the

game is over. Sue rolls first, if she doesn't roll a 6, Bob rolls the die, if

he doesn't roll a 6, Sue rolls again. They continue taking turns until one of

them rolls a 6.

Bob rolls a 6 before Sue.

What is the probability Bob rolled the 6 on his second turn?

**EGG PROBLEM:** *(asked during a software engineering job interview)*

you have two eggs

dino eggs, very resiliant

they will absorb a certain amount of force with no negative consequences

but at some point they crack

if they don't crack, they are fine.

so you're on a 100 story building, you got 20 trials (you're allowed at most 20

individual egg drops) and 2 eggs, is it possible to devise a testing algo that

guarantees to tell you at exactly what floor the eggs will break?

drop an egg and it doesnt break -> 19 trials, 2 eggs left

drop an egg and it does break -> 19 trials, 1 eggs left

More logic puzzle/problems can be found at:

http://psthomas.com/LogicPuzzles.html

http://wiki.xkcd.com/irc/Puzzles

stuart.powers@gmail.com