**FOUR** and

**NINE** 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.