N is a positive integer less than 2015.
Find all values of N such that:
N is equal to precisely 36 less than the square of the sum of digits of N.
***As an extra challenge, solve this puzzle without using a computer program assisted method.
solved analytically for 2-digit N=1Oa+b:
getting a=6 if b=4 and a=4 if b=5
did not try for larger numbers, involving 3 unknowns-
leave it to others.