1986 AIME Problem 10

In a parlor game the “magician” asks one of the participants to think of a three-digit number (a b c), where a, b and c represent digits in base 10 in the order indicated. Then the magician asks this person to form the numbers (a c b),(b a c),(b c a),(c a b) and (c b a), to add these five numbers, and to reveal their sum, N. If told the value of N, the magician can identify the original number, (a b c). Play the role of the magician and determine (a b c) if N=3194.