Permutations and Combinations of Solution sets

Hello Everyone (and anyone haha)!!

I'm solving a problem for class, in which the equation is:

= 1

****J1-J5 are different variables, they're not being multiplied.

My teacher told us to essentially create an excel sheet, and keep guessing the inputs until our outputs equal 1, but I feel like there has to be a way to design a program/code block that can provide sets of working permutations and combinations of correct solution sets, rather than continuously guessing.

Any suggestions? Thanks!!

Answer 1

[Jose Vazquez]

This is his solution, if this provides an explanation to what I'm saying