Question 252284
It appears that 5153 will be the smallest.

Step 1: start with F + F. This creates and even number, so we add 1 to get an odd. That means that O + I is 10 + I.
step 2: In order to get O + I = 10 + 1 there needed to be a carry over from u + v.
step 3: R + E = E, this means that r = 0.

we have
(i) R + E = E - -> 0 + E = E
(ii) U + V = 10 + N
(iii)O + I + 1 = 10 + I - - > 9 + I + 1 = 10 + I
(iv) F + F = N - - > 1 + F + F = N

Let F = 2. N = 5. 
U + V = 15; 8 + 7 = 15. I want to use numbers that don't over lap.
1 + 9 + I = 10 + 1 - -> I = 1.

N=5, I = 1, N = 5, E must be 3 to answer our question.
So, we get 5153.