A Magic Trick
Source:
December 22, 2005
Problem Statement
In a parlor game, the magician asks one of the participants to think of a three digit number (abc) where a, b, and c represent digits in base 10 in the order indicated. The magician then asks this person to form the numbers (acb), (bca), (bac), (cab), and (cba), to add these five numbers, and to reveal their sum, . If told the value of , the magician can identify the original number, (abc). Play the role of the magician and determine the (abc) if .