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
