/sci/ - Science & Math

Give me what you got.

Riddle #1 (easy-medium):
There is a line of people wearing black and white hats. Each person doesnt know which color their hat is and they don't know which color the people behind them wear. One at a time, every person shouts "black" or "white" from the last person in the line (the one that can see all hats but not his own) until the first one.
Their job is to shout the color of the hat that they are wearing except the last one, which doesn't have to say the correct color.
How do they make that possible?

Riddle #2 (hard):
There are 3 rooms.
Room 1: 2 people
Room 2: 100 drawers numbered 1-100, each drawer has inside it a number between 1 and 100, no duplicates.
Room 3: Empty
Person 1 goes out of room 1 and into room 2. He can look inside the drawers all he want. After he made his calculations he can switch the numbers between 2 drawers (1 switch) and then he is escorted out to the 3rd room.
Person 2 goes into room 2 and is given a random number between 1 and 100. His job is to find that number within 50 drawer openings.
When they are on room 1 they both know what is about to take place but they don't know which drawer has which number and they don't know what random number is going to be given to person 2.
How do they make this possible?