The Three Groups

Unreviewed import — a classic from the public domain; its solution has not been machine-checked yet.

math

There appeared in "Nouvelles Annales de Mathématiques" the following puzzle as a modification of one of my "Canterbury Puzzles." Arrange the nine digits in three groups of two, three, and four digits, so that the first two numbers when multiplied together make the third. Thus, 12 × 483 = 5,796. I now also propose to include the cases where there are one, four, and four digits, such as 4 × 1,738 = 6,952. Can you find all the possible solutions in both cases?

Solution

Commit an attempt to unseal the proof. Write your answer — right or wrong, thinking it through is the point.

Solution

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