You're still missing the point of these problems, which is to challenge you to come up with a clever proof rather than brute-force the solution.
dhosek understood the assignment by making an argument that 123456789 is composite without relying on explicit division of a 9-digit number, which most people would find rather difficult to do in their heads.
Similarly, the posted link is about tiling a mutilated chessboard with dominos. Tiling problems in general are NP-hard, so clearly this isn't something you can solve in your head _in general_, but the charm of that specific problem is that you _can_ solve it by making an insightful observation to avoid the brute force computations.
Similarly, for the puzzle you complained about: we are asked to find 1/a + 1/b where a × b = 37 and a + b = 18. The general solution is to solve a system of two linear equations which involves solving a quadratic equation, which is possible, but tedious and difficult to keep in your head, but the entire point of the question is that there is a better way to figure out the result.
dhosek understood the assignment by making an argument that 123456789 is composite without relying on explicit division of a 9-digit number, which most people would find rather difficult to do in their heads.
Similarly, the posted link is about tiling a mutilated chessboard with dominos. Tiling problems in general are NP-hard, so clearly this isn't something you can solve in your head _in general_, but the charm of that specific problem is that you _can_ solve it by making an insightful observation to avoid the brute force computations.
Similarly, for the puzzle you complained about: we are asked to find 1/a + 1/b where a × b = 37 and a + b = 18. The general solution is to solve a system of two linear equations which involves solving a quadratic equation, which is possible, but tedious and difficult to keep in your head, but the entire point of the question is that there is a better way to figure out the result.