Game show with 3 prizes
Source: 2009 AIME I #9
March 18, 2009
AMCAIME
Problem Statement
A game show offers a contestant three prizes A, B and C, each of which is worth a whole number of dollars from to inclusive. The contestant wins the prizes by correctly guessing the price of each prize in the order A, B, C. As a hint, the digits of the three prices are given. On a particular day, the digits given were . Find the total number of possible guesses for all three prizes consistent with the hint.