This is a follow-up question to Does this mathy square have any solutions? (And how many?)Does this mathy square have any solutions? (And how many?).
Consider a 7x7 grid of math operators o and numbers A, B, ..., P:
A o B o C o D
o o o o o o
E o F o G o H
o o o o o
I o J o K o L
o o o o o o
M o N o O o P
This grid encodes 10 math equations. There are 4 horizontal equations, 4 vertical, and 2 diagonal. Specifically:
A o B o C o D
E o F o G o H
I o J o K o L
M o N o O o P
A o E o I o M
B o F o J o N
C o G o K o O
D o H o L o P
A o F o K o P
D o G o J o M
Note that the central operator o at position (4,4) is shared by both of the diagonal equations.
The question is: Can the letters A through P be replaced with all distinct numbers 1 through 16 in any order, and the placeholder operators o by + or * or = such that all 10 grid equations are satisfied? Operator precedence is the usual, no grouping is allowed.
Are there lots of solutions or none at all?
