You are at a casino in Vegas and you have earned 99 chips by playing poker!
While you are checking out a slot machine, someone comes to you and congratulates you that you have a chance to make more chips by using your own chips into a strange four slot machine.
With this machine, you can put as many coins as you want into the four slots available and pull the trigger only once to make more coins but all four slots where you put your coins in the machine behave differently:
- One of them makes your coins four times as many as before!
- Another slot just gives your coins back.
- The last two slots do not give your coins back at all.
But you do not know which slot is which and you can take your coins back after pulling the trigger from somewhere else as a whole.
At most how many coins can you guarantee to have at the end when playing with this machine?
Answer
Quick lower bound:
If you were to
Evenly divide the chips between the four slots (24 in each, with 3 left over), you would get 96 from one, 24 from another, and 0 from the others, for a guaranteed 123 chips in the end.
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