There are no illogical problems however, there are many problems that seem irrational and there is a difference between the two.
Digital business and society become over complex and extremely uncertain, business problems are also like jigsaw puzzles, sometimes make you feel the lack of clues, at the world with so many flavors of analytics, is there something like an “illogical” problem, if so, how to solve it?
It is difficult to encounter a 'real world' (physical/commercial) problem whose solution does not follow any logic at all. Often, the apparent 'illogical' nature of our original perception of the problem may be masking a rationale that we just cannot comprehend. We all use our creativity to solve problems for what is creativity about, an ability to seek solutions to problems. There is no guarantee of a correct answer, just an attempt to find one. It's how we learned to walk and talk for example.
There are no illogical problems however, there are many problems that seem irrational and there is a difference between the two. Some problems seem irrational as they are caused by people’s emotional reaction to a set of circumstances or events. This can appear to be illogical. Many people find it difficult understanding that the irrational is very common and is often a fear response to change or preserved threat. Perhaps the nature of how the "implementation of the idea has to follow a logical path for the solution" may include devices such as pattern recognition... We have a predisposition to seeking patterns (potentially in the pursuit of logic) when attempting to 'find' a solution whether the pattern-seeking follows more conventional structures (common qualities, correlates within each modality, self-evident relationships etc), or more divergent methods has a direct relationship to our creative potential.
The original germ of a creative idea is often, if not always arrived at through the interaction of ideas from different domains of thought and experience (is inherently 'illogical,' if you like). The implementation of the idea has to follow a logical path to the solution of most types of problem (since contemporary society tends to follow logical rather than lateral kinds of structures). Therefore, the actual solution to a problem requires both cross-domain (divergent) cognitive processes as well as logical, convergent ones.The process may not conform to any known logic, as it can wander and be influenced by disparate associations brought up during the act of exploring (the rationale between the steps may not have been predictable).
If, there are such an “illogical problems,” the resolution of an illogical problem requires a logical process, but the source of the information that permits this logical conclusion might function in an abstract manner. At the macro level, however, it does conform to a sequence, a focus or a goal, a motivation to explore proposals, a willingness to imaginatively explore, an ability to evaluate the imaginative proposals for 'appropriateness' and a capacity to translate those ideations into some form of unambiguous result.