Since E is a positive base 10 digit, it follows that each of V(PIE) and V(PI) is a positive integer, so that each of PI and PIE is a perfect square.
This is possible whenever:
(PI, PIE) = (16,169), (25,256) and (36,361)
Now:
(PI, PIE) = (16, 169) gives: V(PI) +E = 4+9=13=V(169)= V(PIE)
(PI, PIE) = (25, 256) gives: V(PI) +E = 5+6=11=V(121) /= V(PIE), a contradiction
(PI, PIE) =(36,361) gives: V(PI) + E = 6+1=7= V(49) /= V(PIE), contradiction.
Consequently, (P, I, E) =(1,6,9) is the required solution to the given alphametic.
Edited on January 8, 2022, 10:09 pm
Puzzle Solution
