What do you do when you encounter a seemingly-unsolvable problem? Do you have a go-to technique that helps you break through? Please consider the following anecdote (known as Dunker's Radiation Problem, originally developed in the 1930's) that keeps cropping up in my research. It highlights a technique that our students have found enormously value. (This particular version is taken from Dave Epstein's "Range")

"Suppose you are a doctor faced with a patient who has a malignant stomach tumor. It is impossible to operate on this patient, but unless the tumor is destroyed, the patient will die.

"There is a kind of ray that can be used to destroy the tumor. If the rays reach the tumor all at once in a sufficiently high intensity, the tumor will be destroyed. Unfortunately, at this intensity, the healthy tissue that the rays pass through on the way to the tumor will also be destroyed. At lower intensities the rays are harmless to healthy tissue, but they will not affect the tumor either.

"What type of procedure might be used to destroy the tumor with the rays and at the same time avoid destroying the healthy tissue? It's on you to excise the tumor and save the patient, but the rays are either too powerful or too weak. How can you solve this?

"While you're thinking, a little story to pass the time: there once was a general who needed to capture a fortress in the middle of a country from a brutal dictator. If the general could get all of his troops to the fortress at the same time, they would have no problem taking it. Plenty of roads that the troops could travel radiated out from the fort like spoke-wheels, but they were strewn with mines, so only small groups of soldiers could safely traverse any one road.

"The general came up with a plan. He divided the army into small groups, and each group traveled a different road leading to the fortress. They synchronized their watches, and made sure to converge on the fortress at the same time via their separate roads. The planned worked. The general captured the fortress and overthrew the dictator.

"Have you saved the patient yet? Just one last story while you're still thinking: years ago, a small town fire chief arrived at a woodshed fire, concerned that it would spread to a nearby house if it was not extinguished quickly. There was no hydrant nearby, but the shed was next to a lake so there was plenty of water. Dozens of neighbors were already taking turns with buckets throwing water on the shed, but they weren't making any progress.

"The neighbors were surprised when the fire chief yelled at them to stop, and to all go fill their buckets in the lake. When they returned, the chief arranged them in a circle around the shed, and on the count of three had them all throw their water at once. The fire was immediately dampened, and soon thereafter extinguished. The town gave the fire chief a pay raise as a reward for a quick thinking.

Are you done saving your patient? Don't feel bad, almost no one solves it. At least not at first, and then nearly everyone sells it."

Here's the kicker:

"Only about 10% of people solve Dunker's Radiation Problem initially. Presented with both of the radiation problem and the fortress story, about 30% solve it and save the patient. Given both of those plus the fire chief story, half solve it."

And how do you dramatically increase the odds of solving the puzzle?

"Given the fortress and the fire chief stories and then told to use them to help solve the radiation problem, 80% save the patient."

These numbers highlight an important point: deliberately trying to leverage a relevant analogy dramatically increases the likelihood of a breakthrough on an insight challenge.

Related: On Randomness

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