Could Einstein's riddle be solved easier with an equation?

BillyBob1

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Eisntein's 'who own the fish' riddle.

I keep looking at it and thinking that it would be so much easier with an equation. Would it work if I made it into a big equation with Brit=red, Swede=dog, Green<White, etc.? Would that yield a decent answer, or am I just being too hopeful?
 
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