Please help me solve this cryptarithm. I will be grateful and you will earn 10 points.

Step-by-step explanation:

First, S must be 4, as if S was 5 the sum would be a 4 digit number.

T+N should be greater than 10 as we want to find the maximum.

Similarly, A+U must be greater than 10, making O equal to 9

We know that A+U-10 = T+N if T+N is less than 10 -- if T+N is greater than 10, A+U-10 = T+N - 10

Writing a quick python script that's not the cleanest nor most concise, I have

import pandas as pd

sols = []

sols_combos = []

num_sols = 0

for a in range(0, 10):

   for u in range (0,10):

       for t in range(0,10):

           for n in range(0,10):

               if (len({a,u,t,n}) == 4) & (4 not in {a,u,t,n}) & (9 not in {a,u,t,n}):

                   if (a+u >= 10):

                       if (t+n >= 10):

                           if ((a+u-10) == (t+n-10)):

                               sols.append(a+u-10)

                               sols_combos.append([a,u,t,n])

                               num_sols += 1

                       else:

                           if ((a+u-10) == (t+n)):

                               sols.append(a+u-10)

                               sols_combos.append([a,u,t,n])

                               num_sols += 1

list_max = [i for i, x in enumerate(sols) if x == max(sols)]

pd.Series(sols_combos).loc[list_max]

as my script.

the maximum I get for F is 5, and the solutions, in terms of A, U, T, and N are as follows:

[7, 8, 0, 5]

[7, 8, 2, 3]

[7, 8, 3, 2]

[7, 8, 5, 0]

[8, 7, 0, 5]

[8, 7, 2, 3]

[8, 7, 3, 2]

[8, 7, 5, 0]

This means that F is 5

9

step-by-step explanation:

where are the choices?