You have five 1's at your disposal, together with five arithmetic operations of your choice. However, as you only have five operations, you should choose them wisely.
Question: What is the largest integer that you can generate this way?
- Numbers can not be infinite. No dividing by 0.
- You cannot concatenate the 1's (i.e. you cannot use two 1's to make 11)
- You cannot use any other numbers in any other form: no Greek alternatives, no constants such as $e$ or $\pi$.
- Parentheses come for free; you may use as many as you like.
- You may use two or more operations in a row
- You may use any notation you would like. One solution below uses "Knuth's Up Arrow Notation". Each arrow uses one operation of the five allowed operations.
1+1+1+1++1 = 5 ((1+1+1)↑↑(1+1)) = 27 <-- Uses Knuth's Up Arrow Notation (1+1)^((1+1+1)!) = 64 ((1+1+1)!)^(1+1) = 81
I have posted my solution below, let's see if you can beat me!