The proof that you’ve nailed the problem is that people will give you their money.This can be restated as a conditional sentence:
If you have solved the problem, then people will give you their money.This sounds correct. The contrapostive of this statement has the exact same truth value:
If people will not give you their money, then you have not solved the problem.While the inverse and the converse may indeed be true, their logical truth does not depend on the logical truth of the original statement, so I will not confuse the issue by going through them.
Now, lets suppose that you are running a business or organization and Nathan Furr's statement is not only true but true of your business. You have solved a problem and so people are giving you money. Let's say you change something in the business and people stop giving you money. If people will not give you their money, then you have not solved the problem. Whatever you were doing before must have been solving the problem. Whatever you changed must have made your product or service cease to solve a problem and so people have stopped giving you money.
But whoever said that business decisions were necessarily logical.