Kenny Albright, Mike Behrens, Nathan Pauli, Ray Kremer
Correct solutions were also sent in by Bradley student Benjamin Brown
and Bradley faculty member Ollie Nanyes. Correct solutions
were also received from Aaron Kahn, Yan Fridman, Will Troxel, Cyril
Terakopiantz, Richard Oak, Burkhart Venzke, Robert McQuaid, Jeffrey
Szymona, Brian Laughlin, Sandy Harmasz, Alan Zimmermann, Brian P. Glover,
Tim Kelley.
The answer is yes!
The product of the integers from 1 to 9 is 362880. If all three sets formed a product less than 71, the product of the three would be no larger than 713 = 357911, which is too small.
One can come close. The partition {9,8}, {6,4,3},
{7,5,2} (with the 1 being put anywhere) gives products 72, 70, 70.
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