card game with 1-9, split in 3 persons. given relation with product and sum
Source: Cono Sur 2002 P1
August 1, 2018
number theoryconsecutiveSums and Productscono sur
Problem Statement
Students in the class of Peter practice the addition and multiplication of integer numbers.The teacher writes the numbers from to on nine cards, one for each number, and places them in an ballot box. Pedro draws three cards, and must calculate the sum and the product of the three corresponding numbers. Ana and Julián do the same, emptying the ballot box. Pedro informs the teacher that he has picked three consecutive numbers whose product is
times the sum. Ana informs that she has no prime number, but two consecutive and that the product of these three numbers is times the sum of them. What numbers did Julian remove?