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Puzzling

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  • $\begingroup$ General: It's not THAT horrible and relative quick to prove. Let the counter sides be 16,25,34. Then $t1*t3*t4-t2*t3*t4-t1*t2*t5+t2*t3*t5+t2*t4*t5-t3*t4*t5+t1*t2*t6-t1*t3*t6-t1*t4*t6+t3*t4*t6+t1*t5*t6-t2*t5*t6=0$ $\endgroup$ Commented Jul 14 at 18:33
  • $\begingroup$ Partial answer to bonus: I'm stoopid. Since virtually all of my equations I ever encountered in my recreational math are homogenous, I also assumed these are. They aren't. Which means than any "accidental" rational solution can be scaled. One of the 6 solutions happens to be always rational (regardless of the wurzelrider), the rest of the solution way is routine. $\endgroup$ Commented Jul 19 at 15:06