are square numbers, both have the same sum of digits i.e. IN
ONE is not a square, but its s.o.d. is. It equals IE.
Each of the bold letters represents a digit in a one-to-one correspondance.
What is the value of FINE?
a) O+N+E = 10*I + E, so O+N = 10*I, so I = must equal 1
b) IE is square, so E must = 6
c) N+I+N+E = 10*I + N, so 2*N +7 = 10 + N, so N = 3
Checking, NINE = 3136 = 56^2.
We did not need to know that this was square to solve the alphametic.
d) O + N = 10, so O = 7
e) F+O+U+R = 13, so F+U+R = 6
Since 1 and 3 are accounted for, this can only be 0, 2 and 4 in some order.
FOUR must equal 2704 or 2740 or 4702 or 4720.
Only 2704 is square, being 52^2.
f) So FINE = 2136. It is not square, and neither is its s.o.d.