MathDB
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 11 to 99 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 55 times the sum. Ana informs that she has no prime number, but two consecutive and that the product of these three numbers is 44 times the sum of them. What numbers did Julian remove?