Linear Diophantine Equation #1

Linear Diophantine Equations
  1. B + A = 6
  2. E + B = C
  3. E + C + B = 8

Hint

Answer

We can see that we can substitute equation 2 in 3, which would result in
3. C + C = 8, so we know that C = 4

Therefore we now now:
  • B + A = 6
  • E + B = 4
Which tells us:
  • A - E = 2
So, A > E. We can have either A = 5, E = 3, or A = 3, E = 1.

With A = 5, E = 3, we would have B = 1.
A = 3, E = 1, we would have B = 3.

The first solution gives us unique values for all characters, the second solution doesn't.

Therefore, we have the solution:
  • A = 5
  • B = 1
  • C = 4
  • D = 2
  • E = 3