We are four against the masses. We are trying to find the one who is the whole package. We sigh, we laugh, we frown while we hope that the next one will be the one. Who are we?
Three brothers share a family sport:
A non-stop marathon
The oldest one is fat and short
And trudges slowly on
The middle brother’s tall and slim
And keeps a steady pace
The youngest runs just like the wind,
A-speeding through the race
“He’s young in years, we let him run,”
The other brothers say
“‘Cause though he’s surely number one,
He’s second, in a way.”
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.