Consider a $5\times5$ grid of math operators and numbers that encodes 8 math equations:
A + B = C = + + + + D + E = F + = = = = G = H + I
There are 3 horizontal equations, 3 vertical, and 2 diagonal. Specifically:
A + B = C D + E = F H + I = G D + G = A B + E = H C + F = I A + E = I C + E = G
However, to make the grid less strict, each equation has 3 additional allowed forms:
+can be replaced with
A * B = C. (We'll avoid
- / ^since they aren't commutative.)
=can be swapped. e.g.
A = B + C.
Both of the above. e.g.
A = B * C.
Thus you can massage the equations a bit in order to form a more workable grid. For example, it might look like:
A * B = C + = * * + D = E * F = = = + = G * H = I
The question is: Can the letters
I be replaced with all one-digit numbers
9 in any order such that all 8 grid equations are satisfied?
Are there lots of solutions or none at all?
(Bonus: What if
^ is allowed to be an operator (and you make some assumptions about reading direction).)