Linear Diophantine Equations with Constraints

  1. #1
  2. #2
  3. #3
  4. #4
  1. Linear Diophantine Equations
Click category to hide/unhide questions

#1

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

Hint

No 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

Linear Diophantine Equations with Constraints are a type of mathematical problem where you are given a set of linear equations with integer coefficients, and you are asked to find unique integer solutions that satisfy the linear equations. These puzzles are a unique fusion of mathematical reasoning and logic. Your task is to deduce the distinct values of these variables based on the provided sum equations. These puzzles challenge your ability to analyze patterns, solve equations, and manage constraints simultaneously. Try to solve them as quick as possible, because during an interview you will be timed as well!

For all questions, you have the constraint that A – E need to be unique integers in the range of 1 – 5.