#### youre_a_squib_now

##### Inkling Fleet Admiral

- Joined
- Jan 30, 2024

- Messages
- 696

- Switch Friend Code
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so in the meantime, here's something random my brain thought of. See if you can figure it out.

I created a system that can represent any integer greater than or equal to 2 using only parentheses. The parentheses are always nested properly (meaning that the number of opening and closing parentheses are the same and that the set of parentheses to the left of a given parenthesis always contains at least as many opening parentheses as closing parentheses); incorrectly nested parentheses do not represent a number and are invalid. A single integer may correspond to more than one string of parentheses, but every valid string of parentheses corresponds to exactly one number.

Here are some examples.

10 = ()((()))

23 = ((())(()))

39 = (())(()(()))

73 = ((()())(()))

86 = (()(()()))()

127 = (((((())))))

The goal is to figure out how it works. Show that you have figured it out by converting (())(()((()()(())(()())))) to a regularly-formatted number.

idk how hard this is going to be so I might drop hints and/or more examples periodically, we'll see