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Linear Diophantine Equation #2
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 quickly 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.
For all questions, you have the constraint that A – E need to be unique integers in the range of 1 – 5.
- A + D = C
- E is not 5
- D + E = B + C
- D + 1 = C
Solution
The easiest conclusion is found by looking at Equation 1 and Equation 4. There, we can directly see that:
- A = 1
- E - 1 = B.
- E can only be either 3 or 4
- B can only be either 2 or 3
- A = 1
- B = 2
- C = 5
- D = 4
- E = 3
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