the value of mental models - lateral thinking

from Wikipedia

Example 1

It took two hours for two men to dig a hole five feet deep. How deep would it have been if ten men had dug the hole for two hours?..............

The answer appears to be 25 feet deep. This answer assumes that the thinker has followed a simple mathematical relationship suggested by the description given, but we can generate some lateral thinking ideas about what affects the size of the hole which may lead to different answers:

A hole may need to be of a certain size or shape so digging might stop early at a required depth.

The deeper a hole is, the more effort is required to dig it, since waste soil needs to be lifted higher to the ground level. There is a limit to how deep a hole can be dug by manpower without use of ladders or hoists for soil removal, and 25 feet is beyond this limit.

Deeper soil layers may be harder to dig out, or we may hit bedrock or the water table.

Are we digging in soil? Clay? Sand? Each presents its own special considerations.
Holes required to be dug beyond a certain depth may require structural reinforcement to prevent collapse of the hole.

Digging in a forest becomes much easier once we have cut through the first several feet of roots.

Each man digging needs space to use a shovel.

It is possible that with more people working on a project, each person may become less efficient due to increased opportunity for distraction, the assumption he can slack off, more people to talk to, etc.

More men could work in shifts to dig faster for longer.

There are more men but are there more shovels?

The two hours dug by ten men may be under different weather conditions than the two hours dug by two men.

Rain could flood the hole to prevent digging.

Temperature conditions may freeze the men before they finish.

Would we rather have 5 holes each 5 feet deep?

The two men may be an engineering crew with digging machinery.

What if one man in each group is a manager who will not actually dig?

The extra eight men might not be strong enough to dig, or much stronger than the first two.

The most useful ideas listed above are outside the simple mathematics implied by the question.

Example 2

(this isn't as good as an example, but it shows how good/new/out-of-the-box ideas could come from an exercise like this one)

Consider the statement "Cars should have square wheels." When considered with critical thinking, this would be evaluated as a poor suggestion and dismissed as impractical. The Lateral Thinking treatment of the same statement would be to speculate where it leads. Humor is taken intentionally with lateral thinking. A person would imagine "as if" this were the case, and describe the effects or qualities. Someone might observe: square wheels would produce very predictable bumps. If bumps can be predicted, then suspension can be designed to compensate. How could this car predict bumps? It could be a laser or sonar on the front of the car. This leads to the idea of active suspension. A sensor connected to suspension could examine the road surface ahead on cars with round wheels too. A car could have a sensor for determining when it was going to hit a bump that feeds back to suspension that would know to compensate. The initial "provocative" statement has been left behind, but it has also been used to indirectly generate the new and potentially more useful idea.