Words and Numbers - The Solutions
07/26/2004

If we write out the entire alphabet and then match each letter with its corresponding value, we can see that JULY has a value of 10 × 21 × 12 × 25 = 63,000. That’s a big value for such a little word!

We are trying to find three letter-values with a product of 60. Keep in mind that the greatest possible letter-value is 26. If we look at the prime factorization of 60, and keep in mind that we can use 1 as a factor, too, we will get the following factor-triples that contain factors less than 27: (1,4,15), (1,6,10), (2,5,6), (2,3,10), (3,4,5), (1,3,20), (2,2,15), (1,5,12). Each of these eight factor-triples corresponds to a three-letter combination with a value of 60.

Upon factoring 455, we see that its prime factorization is 5 × 7 × 13. This means that the only factors of 455 that are less than 27 are 1, 5, 7 and 13. According to this, our word must have an E, G and M and could have some A’s. Using just the E, G and M, we can make the word GEM, a precious or semi-precious stone!