In a classic 1942 experiment, American psychologist Abraham Luchins asked volunteers to do some basic math by picturing water jugs in their mind. Given three empty containers, for example, each with a different capacity—21, 127 and three units of water—the participants had to figure out how to transfer liquid between the containers to measure out precisely 100 units. They could fill and empty each jug as many times as they wanted, but they had to fill the vessels to their limits. The solution was to first fill the second jug to its capacity of 127 units, then empty it into the first to remove 21 units, leaving 106, and finally to fill the third jug twice to subtract six units for a remainder of 100. Luchins presented his volunteers with several more problems that could be solved with essentially the same three steps; they made quick work of them. Yet when he gave them a problem with a simpler and faster solution than the previous tasks, they failed to see it.

This time, Luchins asked the participants to measure out 20 units of water using containers that could hold 23, 49 and three liquid units. The solution is obvious, right? Simply fill the first jug and empty it into the third one: 23 − 3 = 20. Yet many people in Luchins's experiment persisted to solve the easier problem the old way, emptying the second container into the first and then into the third twice: 49 − 23 − 3 − 3 = 20. And when Luchins gave them a problem that had a two-step solution—but could not be solved using the three-step method to which the volunteers had become accustomed—they gave up, saying it was impossible.

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