This (writing a program to solve the problem) would be a perfectly valid solution if the model had come up with it.

I participated in a "math" competition in high school which mostly tested logic and reasoning. The reason my team won by a landslide is because I showed up with a programmable calculator and knew how to turn the problems into a program that could solve them.

By prompting the model to create the program, you're taking away one of the critical reasoning steps needed to solve the problem.