A E R O + N E X T = R A R E
A E R O - N E X T = E X I T
=> E=3T (mod 10) O=2T (mod 10) (supposing same value for T in all words implicated: if no results should be found we will revoke these suppositions)
so T O E (possible values)
1 2 3
2 4 6
4 8 2
6 2 8
7 4 1
8 6 4
but
A E R O R A R E
+ = +
A E R O E X I T
=>either or E+T=10+2O or E+T+10=2O in the first case R=I+1 in the second case I=R+1. In both cases I, R neighboring digits
E+T+10=2O => T O E = 4 8 2 (with E+ T =10 + 2O is also possible T O E = 6 2 8 but E value is very high, see below)
Also:
A E R O + N E X T = R A R E
A E R O - N E X T = E X I T
=>R>A>(N,E)
Collecting results:
X=9
T O E=4 8 2
I=R+1 e R>A>(N,E)
Ordering letters:
X=9; O=8; I=7; R=6; A=5; T=4; and E,N=3,2,1
But as N has unique value => either: or (E=3 / 2 and N=1) or (N=3 and E=2 / 1)
Solution
X=9; O=8; I=7; R=6; A=5; T=4; E=3, 2; N=1
Solution explained
