Linear Diophantine Equation #2

Linear Diophantine Equations
  1. A + D = C
  2. E is not 5
  3. D + E = B + C
  4. D + 1 = C

Hint

Answer

The easiest conclusion is found by looking at Equation 1 and Equation 4. There, we can directly see that:
  • A = 1
Subtracting Equation 4 from Equation 3 results in:
  • E - 1 = B.
Since E is not 5 or 1, and B (= E - 1) can't be 1 as well:
  • E can only be either 3 or 4
  • B can only be either 2 or 3
D and C are also 2 sequential numbers (D + 1 = C), which can only be the case if B and E hold the values 2 and 3, such that 4 and 5 are not assigned to a character yet. So, after confirming it with the set of equations, we have the solution:
  • A = 1
  • B = 2
  • C = 5
  • D = 4
  • E = 3