So remember all those puzzles about 100 or 1000 or however many logicians abducted by aliens and they are going to be killed if they can't figure out their hat color or the number on their back? Well it turns out you were such a bright mind that the aliens abducted you, and luckily you were one of the logicians that survived.
Unfortunately, instead of taking you back home, they just left you in a room with all the other logicians that survived. Escaping doesn't seem very likely any time soon because right now everyone is focusing on getting food every day. There is a single fridge in the corner of the room but it is one of those newfangled fridges and it has a security code that you have to put in to open it. The fridge has a panel on the top that displays 5 digits, and those digits change every day, along with the fridge restocking. The problem is that when the fridge restocks, the security code changes. For the first six days, you've had to brute force the code by just typing every combination in until you get it (only 100000 combinations, not too bad), but you really need to figure out what the pattern is for the codes so you can focus on escaping instead of cheeseburgers.
The panel numbers and codes for that day are as follows:
Panel -- Code
12345 = 56306
04418 = 35129
20530 = 65048
54472 = 68425
00000 = 00000
60454 = 95126
29830 = 39175
00000 = 03334
08224 = 35386
14412 = ?????
Today the panel says 14412. Can you figure out the code and what the algorithm is so you can get the food easily each day?
About the brute-force method: Pertaining to David James' comment,the brute force method started with 00000 on the fifth day, but it does not follow the pattern of 00001, 00002... One logician is in charge of the brute-forcing and each day he starts with the panel number, and then does what seems like a random sequence. At least that's what you all think... he's been a little bit looney since the abduction but you all let him use his "sequence" to make him happy.
Yesterday in the fridge, someone found a fortune cookie which contained the following fortune:
Look backwards to go forward
It's probably just a generic fortune mass produced in a cookie factory, but what if it's a clue about solving the code?
Another fortune cookie has shown up:
What could those numbers be referring to?
More fortune cookies:
Codes to a day need not connect
But codes to the panel need be
Look how to get panel from code
And you'll be able to get free
Last fortune cookie:
There can be more than one, but each can't be more than once.
Days passed: 9 (seems like a lot more though)
Note: Please post partial answers if you think you have anything so I can see where you are having problems