Linear Diophantine Equation #3

Question

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.

 	D - 2 = C
 	E + C = D
 	A + E = C

Accepted Answer

Adding up Equation 1 and Equation 2 results in:
D + E - 2 + C = C + D, which is equal to E - 2 = 0

Therefore, we can conclude that:

 	E = 2

In Equation 3, we can see that:

 	A + 2 = C

However, we also know that C + 2 = D, so we have an order of A < C < D, all increasing 2 in value. Given that the numbers are in a range of 1-5, the only possible solution is:

 	A = 1
 	C = 3
 	D = 5

We already know that E = 2, so the only remaining solution is that:

 	B = 4.

This solution works for all equations. So, the solution is:

 	A = 1
 	B = 4
 	C = 3
 	D = 5
 	E = 2

Title	Category	Subcategory	Difficulty	Status
Linear Diophantine Equation #1	Math Questions	Solving Unknowns	Medium	Example
Linear Diophantine Equation #2	Math Questions	Solving Unknowns	Medium	Example
Linear Diophantine Equation #4	Math Questions	Solving Unknowns	Medium	Unlock
Long Fish	Math Questions	Solving Unknowns	Medium	Unlock
Product of Unknowns #1	Math Questions	Solving Unknowns	Hard	Unlock
System of Weights	Math Questions	Solving Unknowns	Medium	Unlock

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The Interview Guide for Quants and Traders