Integer Constraint Search Algorithm

This project implements a brute-force search algorithm in C to solve a specific cryptarithmetic problem. It iterates through permutations of a 6-digit number ($ABCDEF$) to find values that satisfy a strict set of number theory constraints.

🎯 Problem Definition

The algorithm searches for a 6-digit integer $N$ represented as digits $A,B,C,D,E,F$ that satisfies ALL of the following logical conditions simultaneously:

1. Uniqueness: All digits ($A, B, C, D, E, F$) must be distinct.
2. Perfect Square: The number formed by the last two digits ($EF$) must be a perfect square ($x^2$).
3. Perfect Cube: The number formed by the first three digits ($ABC$) must be a perfect cube ($y^3$).
4. Linear Relation: Digit $A$ must be equal to $E + 1$.
5. Divisibility: The number formed by the first two digits ($AB$) must be divisible by 3.
6. Primality: The number formed by digits $D, E, F$ ($DEF$) must be a Prime Number.

⚙️ Technical Implementation

• Language: C (Standard Library only, no external dependencies).
• Approach: Nested Loops (Exhaustive Search / Brute Force).
• Optimization: The algorithm uses conditional continue statements to prune the search tree early. For instance, if the uniqueness constraint fails early, inner loops are skipped to save computational power.
• Manual Math Logic: Includes a custom implementation for primality testing (is_prime logic inside the loop) without using <math.h> functions, demonstrating low-level logic building.

🚀 How to Run

1. Compile the code using GCC:

   gcc solver.c -o solver

2. Run the executable:

   ./solver

3. The program will output the 6-digit number(s) satisfying all criteria.

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This repository demonstrates algorithmic thinking and control flow management in C.