If you use the word "and" in naming numbers above 100, then, for example, 999 is named "nine hundred and ninety-nine". Considering this as four words, one of them hyphenated, the letter counts in the four words are 4, 7, 3 and 10. The product of these four numbers is 840.

There is one 3-digit number such that if you apply the above procedure, the final product of its four word lengths is the same as the original number. What is that number?

Similar to Ady's solution I mapped the letter counts within a spreadsheet with one difference.

The problem text offers a hyphenated word as the last word of four but the next sentence to me suggests only to treat hyphenated words as one word meaning that words for unit digits are allowed.

As such, for that values that Ady has for C, my set also includes those which he had for A. 

Those additional values however had no impact on the required result of 693.

Posted by brianjn on 2010-07-31 04:50:04