Lists Help? (How could I get the highest possible score?)

Hello, I have a thing that I am trying to figure out. I have made a game where you make a list of 15 numbers from 1-15. You write your first number. Then you write a second number, and if the number is greater, you multiply them, if the number is lower, you divide them. How could I get the highest possible score? And, you cannot make numbers in sequence. I’ve tried 1 to 15, my final score is 1. I’ve also tried 2, 3, 4,5,6,7,8,9,10,11,12,13,14,15,1, but that does not work either. What should I do to get a higher score?

NathanAdamson said:

Hello, I have a thing that I am trying to figure out. I have made a game where you make a list of 15 numbers from 1-15. You write your first number. Then you write a second number, and if the number is greater, you multiply them, if the number is lower, you divide them. How could I get the highest possible score? And, you cannot make numbers in sequence. I’ve tried 1 to 15, my final score is 1. I’ve also tried 2, 3, 4,5,6,7,8,9,10,11,12,13,14,15,1, but that does not work either. What should I do to get a higher score?

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First, can you clarify whether they must be 15 DIFFERENT numbers (so that your list is just an ordering of the 15 possible numbers), or a number can be repeated?

Second, does "you cannot make numbers in sequence" mean that no number can be 1 more than the one before it, or that it also can't be 1 less? Or is it something else, such as that no 3 or more can be consecutive?

Also, what do you mean by "I tried 1 to 15"? My first thought was that this meant "1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15" in that order, but the result would not be 1, and it doesn't satisfy your extra rule about not being "in sequence". The same is true of your explicit example. So I'm not really sure what the rules are.

It would seem obvious that, if possible, you'd like to do only multiplications. Both of your examples do that or nearly so, and would give a score of 1,307,674,368,000 if I'm understanding you correctly. You couldn't possibly do better.

Please make the rules as clear as possible, including examples of several "legal" lists and the scores you get.