Two heads may be better than one, but new research suggests that three are even better if the task at hand is solving a logic problem. According to a study published in the April issue of the Journal of Personality and Social Psychology (Vol. 90, No. 4), groups of three, four or five came up with more efficient solutions to a math-based problem than even the best individuals working alone.
In the problem, the letters A through J map to the numbers zero through nine, but not necessarily in that order. To determine which letter belongs to which number, the participants propose equations such as A+B. The researchers respond by telling the students the answer in letter form. If, for instance, the students give the equation A+B, and get B as the answer, they can infer that A equals zero. To solve the problem completely, the students must discover the number-identity for each of the letters within 10 equations, though they are asked to use as few as possible.
Students working alone tended to employ a simple strategy, known as two-letter substitution. Using this strategy, students who know that B equals one might propose the equation B+B to find out which letter equals two.
A more sophisticated strategy—and one hit upon by groups more often than individuals—is multiple-letter substitution. Groups that employ this strategy, for instance, might know that B is one, and ask for an answer to the equation B+BB+BBB+BBBB, or 1+11+111+1,111, and receive the answer of BCDE. Since they know the answer to that problem is 1,234, the participants can map three letters to numbers with a single equation.
The experimenters put 760 college students to the test, randomly assigning them to work alone or in groups of two, three, four or five. The groups of three or more all solved the problem in about six equations. However, groups of two were less efficient—averaging 7.3 equations to map all the letters to numbers. The researchers then looked at the performance of the top individuals among randomly selected sets of two, three, four or five. These top students, working alone, took an average of 6.5 equations to solve the puzzle.
This suggests the best individuals would have done even better if they had been working in groups of three or more, says lead author Patrick R. Laughlin, PhD, a psychology professor at the University of Illinois at Urbana-Champaign.
"The groups put together the partial understanding of the problem that each person had," says Laughlin. "It is not that some genius in the group solved the problems while the others watched."
The finding adds to past research by comparing the average performance of groups with that of the very best individuals working alone, rather than with the average individual's performance, notes Laughlin.