In the picture below the upper path (marked with "1") is the first time you solve the problem. When solving the problem you will learn things and get insights (e.g. Insight A in picture).
If you decide to use another method or tool or approach you might get the middle path (marekd with "2"). Another journey that could possibly lead to the same solution. But in the process you made new insights (Insight B).
Yet another go would be the lower path ("3"). And in that path you will again make new insights. But also possibly solve some other problem. And you might end up with another solution to the original problem. An alternative solution. A solution that might be better than the first you found (using path 1).
Problem solving is a journey. And the methods and tools you select will form the path. Each path could give you unique solutions, new insights and solutions to other problems.
The first solution and problem solving process will of course influence the following attempts. But the new method and tool selected will make the path different anyway. The methods and tools will force you onto a new path. Just like different transportatoin methods will change your real life journey - although destination might be the same.
Another good thing with using mutiple methods is that you gain experience. You learn what methods works best and how to use them. And you can compare and build a toolbox for when to use what...
And you can describe the solutions achieved using different perspectives. Maybe the audience prefer to learn that solution was gained using path 2. Even though you first solved the problem using path 1.
Solving the same problem multiple times can be very rewarding.
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