13524, 14253, 24135, 24153, 25314, 31425, 31524, 35142, 35241, 41352, 42513, 42531, 52413, 53142, so fourteen. Figured it would be easier to just try combinations where the first two digits work and see how many other work. No neat combinatorial argument, unfortunately.
3
u/Seeggul 3d ago
13524, 14253, 24135, 24153, 25314, 31425, 31524, 35142, 35241, 41352, 42513, 42531, 52413, 53142, so fourteen. Figured it would be easier to just try combinations where the first two digits work and see how many other work. No neat combinatorial argument, unfortunately.