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.
Kevin brings his school supplies to the counter. The cashier rings up his purchase for a total of $1.70. Kevin is puzzled, and says, “I bought 2 pencils at 2 cents each, 5 pencils at 4 cents each and 8 notebooks and 12 sheets of colored paper. I don’t remember the prices of the latter two, but the total can’t be $1.70.”