where P$,$ A$,$ G$,$ E are all different single digit number $\{0,1,2,3,...,9\}.$ Obviously, P and E

cannot be $0.$

a$.$ Write down the high$-$order constraints for this equation and the domains of the

carrier digits. $(40$ points$)$

b$.$ Draw the search tree that converts the high order constraints to binary

constraints. $(40$ points$)$

c$.($Extra$)$ Write down a solution. $(5$ extra points$)$