how do machines recognize what kind of dollar bill we're putting in?

Answer 1

Vending machines use a variety of methods to read bills, they check four different characteristics used to verify paper money:

Bills are printed with magnetic ink, and different denominations generate distinctive magnetic fields.
Bills have different conductivities (the rate at which they can conduct low levels of electricity).
Ultraviolet scanning technology can determine the different fluorescent properties of bills.
Digital cameras can reference the optical patterns in bills with a database of authentic patterns.
A vending machine has to verify whether a bill is authentic before it determines its value. The U.S. Bureau of Engraving and Printing hosts this cool fact sheet about the security features used on its currency: color-shifting inks, watermarks, and microprinting.

Those nifty currency counters that you see operated by shady types in gangster movies use a similar array of technology: magnetic sensors, ultraviolet readers, fluorescent bulbs, and optical magnifiers.

Answer 2

I think the serial numbers go with a certain dollar amount or maybe it has a scanner that can read the bill.

Answer 3

Magic