Duncker’s radiation problem reads:
Suppose you are a doctor faced with a patient who has a malignant tumour in his stomach.It is impossible to operate on the patient; but unless the tumour is destroyed the patient will die. There is a kind of ray that can be used to destroy the tumour. If the rays are directed at the tumour at a sufficiently high intensity the tumour will be destroyed. Unfortunately, at this intensity the healthy tissue that the rays pass through on the way to the tumour will also be destroyed. At lower intensities the rays are harmless to the healthy tissue but they will not affect the tumour either. What type of procedure might be used to destroy the tumour with the rays, and at the same time avoid destroying the healthy tissue? (Duncker; 1945; Gick & Holyoak, 1980, 1983; Keane, 1985)
One roadblock to successful performance, even with analogical hints, is understanding how radiation works (Helfenstein & Saariluoma, 2006)
Superficial similarity between analogies, while present in more difficult problems (Reed, 1987; Ross, 1987, 1989) is not found in the Duncker radition problem (Holyoak & Koh, 1987). In general, surface similarity does not effect the number of correct answers, it positively impacts the quality of answers (Heydenbluth & Hesse, 1996)
A story that analogously solves the problem brings a 30% success rate, while no clue provides a 10% success rate (Gick & Holyoak, 1980)
(A bibliography is below the fold)
Gick, M. & Holyoak, K.J. (1980). Analogical problem solving. Cognitive Psychology, 12, 306-355.
Gick, M. & Holyoak, K.J. (1983). Structure-mapping. A theoretical framework for analogy. Cognitive Psychology, 15, 1-38.
Helfenstein, S. & Saariluoma, P. (2006). Mental contents in transfer. Psychological Research, 70(4), 293-303.
Heydenbluth, C. & Hesse, F.W. (1996). Impact of superficial similarity in the application phase of analogical problem solving. The American Journal of Psychology, 109(1), 37-57.
Holyoak, K. J., & Koh, K. (1987). Surface and structural similarity in analogical
transfer. Memory & Cognition, 15, 332-340.
Keane, M. (1985). On drawing analogies when solving poblems: A theory and test of solution generation in an analogical problem-solving task. British Journal of Psychology, 76, 449-458.
Reed, S. K. (1987). A structure-mapping model for word problems. Journal of Experimental Psychology: Learning, Memory, and Cognition, 13, 124-139.
Ross, B. H. (1987). This is like that: The use of earlier problems and the separation
of similarity effects. Journal of Experimental Psychology: Learning, Memory, and Cognition, 13,629-639.
Ross, B. H. (1989). Distinguishing types of superficial similarities: Different effects on the access and use of earlier problems. Journal of Experimental
Psychology: Learning, Memory, and Cognition, 15, 456-468.