THE THREE GROUPS.
(
Money Puzzles)
There appeared in "Nouvelles Annales de Mathematiques" 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 x
483 = 5,796. I now also propose to include the cases where there are
one, four, and four digits, such as 4 x 1,738 = 6,952. Can you find all
the possible solutions in both cases?
Answer:
There are nine solutions to this puzzle, as follows, and no more:--
12 x 483 = 5,796 27 x 198 = 5,346
42 x 138 = 5,796 39 x 186 = 7,254
18 x 297 = 5,346 48 x 159 = 7,632
28 x 157 = 4,396
4 x 1,738 = 6,952
4 x 1,963 = 7,852
The seventh answer is the one that is most likely to be overlooked by
solvers of the puzzle.
