All four numbers must be used for each solution, but they may appear in any order. Permitted:
- the 4 basic mathematical operations,
- square root symbol (maximum twice per solution, and the 2 is implied)
- combining initial numbers by concatenation (eg. 5 and 7 can make 57)
- decimal points, including omitting any initial zero
- repeating decimal bar
- negative number sign.
Not permitted: everything else, including factorials, logarithms, infinite sums, rounding (floor, ceiling), numerical bases other than 10, concatenation of calculation results.
I have created all one hundred but had to use single factorials for seven of them. The missing ones for which non-factorial solutions are needed are 67 (now found), 87, 89 (now found), 91, 92, 94, and 99.