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Largest Product

Using all the digits from 1 to 7, what two numbers have the largest product? For example, 1234 x 567 = 699678 but you can do much better than that.

742 x 6531 = 4,846,002.

A similar problem can be found in L.A. Graham’s Ingenious Mathematical Problems and Methods with a range of 1 to 9, but the principle remains the same – the numbers with the smallest difference produce the largest product. You start out with the highest two digits, 7 and 6, then attach 5 and 4, putting the smaller of the two digits with the larger number, giving you 74 and 65. The next two highest digits are 3 and 2, giving you 742 and 653. Finally, you add the 1 to the lower number. Page 80 has the details of that solution.


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1 Comment on "Largest Product"


Zlatko says
December 13, 2016 @ 22:51

742 × 6 531= 4 846 002
That’s max possible product if you have digits from 1 to 7.


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