1. The problem is to find a method to solve a problem without using brute force. 2. Brute force means trying all possible options until the solution is found, which can be inefficient. 3. Instead, we use problem-solving strategies like algebraic manipulation, pattern recognition, or applying formulas. 4. For example, if solving an equation, use algebraic rules to isolate variables rather than testing all values. 5. If the problem involves searching, use algorithms like binary search instead of checking every element. 6. The key is to understand the problem structure and apply mathematical properties or logical reasoning to reduce the work. 7. This approach saves time and effort compared to brute force.