Strobogrammatic numbers (SNs) are numbers that are the same when viewed upside down: 0, 1, 8, 11, 69, 88, 96, .... These are sequence 000787 at the Encyclopedia of Integer Sequences. This month we consider Strobogrammatic Expressions (SEs): mathematical expressions that describe the same number when viewed upside down. Only the digits 0, 1, 6, 8, and 9, addition, subtraction, multiplication, division, exponentiation, and parentheses are allowed. Here are some simple examples: 91-8/8-16, 68+68+61, and 9(9-6), which describe the numbers 74, 197, and 729 respectively.
Every number can be represented by a SE of the form 1+1+1+.... What are the shortest (in terms of the minimum number of symbols used) SEs that represent the integers from 1 to 100? We are particularly interested in shortest SEs that do not use any SNs.