The probability of your solving the problem is dependent on how you frame it.

Human memory is built to retrieve information related to the cue provided. Sure, we’ve all known and used that radiant thinking process called mind-maps. What we might have missed however is the linkage that radiant thinking has to problem solving. 

Think school and memories around chalk-boards, dusters, wooden desks etc fly into our consciousness. No effort required, just a result from the initial cue. Now if you want to retrieve something, anything else from your memory just change the cue, think food, you will likely think about cuisines, restaurants, cooking despite the fact that you were immersed in the nostalgic world around school-life just a moment ago. 

Herein lies the clue. The key to creative problem solving is the statement of the problem in the form of a cue to memory. That’s what will reach within the recesses of your (& your team’s) memory to draw out the related information. 

In order to pull out a variety of possible solutions to a problem, the problem solver (or group) needs to change the problem statement and the specific mental cues they use to trigger thinking about solutions. 

Let’s take an example - in terms of solving the problem of providing internet connectivity to far flung areas one approach could be about trying to solve the problem of getting the cable upto to the point where the connectivity is required. Possible solutions could range from using current cable infra eg electricity or cable tv and repurposing it to also channelise internet connectivity. Now let’s change the cue- focus on solving for internet bandwidth enveloping the planet (without getting the cable into the problem definition) - the first thing that hits when one talks about enveloping the planet is the atmosphere, space, satellites - most likely the thinking that led to the conceptualisation of Star-link - the disruptive solution spaceX is rolling out to provide via satellite connectivity via a network of hundreds of satellites surrounding the planet.   

Unfortunately there is no ideal route to creating such problem statements, however what we can and must keep in mind is the need to define the problem statement in a variety of ways. Some specific. (eg. solving the lack of cables to drive internet connectivity in remote areas) which will lead to retrieval of specific solutions around cables and cable infra. The group should define the problem in non-specific ways with a more abstract description of the goal (eg. solving for internet connectivity by enveloping the planet with it). Each description, each problem statement will help people, groups, experts recall knowledge that might be distantly related to the domain defined. 

Happy solving!