While strolling home through the industrial district late one night with a puzzle stuck in your head, you wander off course into an area you’ve never been before. As you turn in the direction you think you need to go, two bright machines catch your eye. At first you think they are gambling machines, but upon closer inspection you find a sign which explains it all.
Did you know there are other values of coins besides the ones you are used to? (This is the U.S. so there are coins/bills worth \$0.01, \$0.05, \$0.10, \$0.25, \$0.50, \$1.00, \$5.00, \$10.00, \$20.00) We here at Infinimint deal with coins of all possible values. We prefer to work with the common values, so if it is possible to give you a value which is normal (like a dime, nickel, etc) the machine will do just that.
The two vending machines in front of you have their rules listed on the front:
Insert one coin. Subtract one cent then divide it into three equal-valued coins (Rounded down to the nearest cent).
Insert two coins. Add their values together minus one cent.
You think oh that’s interesting, but it's getting late, I should head home. On your way out, a shiny object on a table catches your eye. You pick it up. It says across the top \$24.99. “Well this is useless”, you think to yourself. No one is going to accept this ridiculous coin for payment. But, you think, maybe there is some way I can get real money out of the vending machines. I should be able to get \$20 easy, maybe even more.
What is the most money in normal values, \$0.01, \$0.05, \$0.10, \$0.25, \$0.50, \$1.00, \$5.00, \$10.00, \$20.00, that can be made from the \$24.99 coin?
I'm not sure what the answer is, but I think it will be apparent if someone has proven that their solution is best.