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Not a common alphametic (Posted on 2016-04-01) Difficulty: 4 of 5
AERO-NEXT=EXIT
AERO+NEXT=RARE

Decode the above alphametic, given:
1. No zeroes appear in the solution.
2. One (and only one) of the letters represents one of two neighboring digits (e.g. R is 7 in some words and 8 in others).

No Solution Yet Submitted by Ady TZIDON    
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Solution explained Comment 2 of 2 |
A E R O - N E X T = E X I T   
no zeroes => X=9 (supposing same value for both E)

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

Edited on April 4, 2016, 3:35 pm
  Posted by armando on 2016-04-04 03:47:15

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