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A puzzle 4U

I live near an airport and a lot of airplanes arrive from every direction and leave in every direction. When I sit in the shade of our house I can see half of the sky, on average what proportion of the airplanes do I see when I am sat there ? 

(Why can't I post picture here ? I have a few more puzzles)

The cold of the floor permeates your throbbing head. You mouth feels like some small creature of the night had used it as a latrine. Trying to open your bloodshot eyes sends a stabbing pain through your retinas that bounces off the inside of your skull making you think your brain will explode. Slowly you pry your sore body off the floor. Your mind slowly dissolves the fuzzy creatures that had taken up residence behind your eyes.

“How did I get here?”

Even the thought causes your bruised intellect to quiver in pain. What is even worse, you slowly remember parts of dinner party last night. You don’t remember all the details, but you do remember drinking way too much, and then offering an off-color toast to your powerful host. Although you thought the toast hilarious, no one laughed. You don’t remember the rest but you know your toast is the reason you are in this dungeon.

You manage to stand and stumble to the table which is the only piece of furniture in the room. Five keys carved from precious stones lie in a pile next to piece of parchment. You recognize the handwriting of your host on the parchment. The note reads:

I hope your wits are as sharp as your tongue. You will need your wits to open the door to this cell. In order to escape you must open the five locks in order using the correct key. You only get one try to open the locks. I don’t think you want to know what happens if you use the wrong order, it will be messy. Here is all the information you need to determine the proper order:

• The ruby key must be used before the obsidian key but after the emerald key. 
• The gold key must be used right after the emerald key. 
• The sapphire key must be used after the obsidian key.

Specify the order you would use in order to escape.

Lets start from smth easy ..) #logic   #math  

11
12
1121
122111
112213
?
?

Now harder:

11
12
1121
122111
112213
?
?

prove, that you'll always get numbers from 1 to 3, and never 4 or more.
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