No, I’m not saying you would know in advance that it was possible, but sometimes you visit the crystal cave and the diamond is just sitting there, so why not work out the odds?

I learned from poking around that checking the invertibility of a system in C is a much, much harder problem than I thought. Nonetheless if that were no object, let’s say coefficients from -16 to 15 (5 bits) times eight terms times choosing up to cubes (64) times three equations is searchable, especially since you have only the final combination of coefficients in the determinant. It’s not impossible to generate the equations like this Fizzbuzz style.

Edit: no. 2048 possible monomials, to the 24th power, not times 24. Fine, can’t brute force it.