Karen owns a restaurant/bar. She wants to attract more customers, and is building her own custom slot machine game, which she can use to give away free drinks or prizes. The more a customer spends, the more spins they get on the slot machine.
She knows that she wants these specs:
- 4 reels on the machine
- All reels must have a different number of symbols, between 2 and 9 inclusively (what the symbols are is irrelevant for this challenge)
- All reels must move (change to another symbol) during a spin.
- All of the symbols on each reel must be unique on that reel.
To avoid using a random number generator, she decides to set each reel to cycle uniformly through each of its possible positions. For example, if a reel has 4 symbols, say, 1,2,3,4, then it will cycle through them in the same pattern, say, 4,2,1,3,4,2,1,3,....
She knows that this guarantees that the machine will cycle through all of its possible states in the exact same order each cycle, but decides that that is OK. She desires to make this cycle as long as possible, to make the machine feel more unpredictable, but she has no idea how to find the correct combination of reel sizes. Although, she does understand that the order of the reels does not matter.
Below is a generic picture of slot machine reels that I found on Google images. It is added only so you get a general idea of slot reels, and is not directly related to this puzzle.
Her friends all have an opinion, and give the following advice about the number of symbols for each reel:
Which friend gave the best advice?
Which friend gave the worst advice?
Can you find a more optimal combination than the best advice?