Which method is more efficient for solving all problems?

[u/Wise_Ad7376]

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1.A naive brute-force method of exhaustively checking all candidates.

2.A method of solving only simultaneous equations using the elimination method (addition and subtraction), and solving all other problems using Method 1.

Method 1 is more efficient than Method 2 for non-simultaneous equation problems because it does not need to consider whether a problem is a system of simultaneous equations. Method 2 solves simultaneous equations quickly, but the proportion of such problems among all problems likely converges to 0.

Note: Here, a "problem" is defined as an algorithm that guarantees the correctness of its answer in finite time, assuming that an answer always exists. This definition was adopted because there are also problems that cannot be solved.

[u/0x14f]

Neither method will solve all solvable problems. Also you need to clarify what you mean by "problem"

[u/Wise_Ad7376 → u/0x14f]

Why can't you solve all the problems? Did you read the entire question?