Question 81
Vitya and Masha play the game. First, Vitya thinks of three different integers. Then Masha can ask one of the following quantities: either the sum of the numbers, or the sum of pairwise products of the numbers, or the product of the numbers suggested by Vitya. Masha asks questions sequentially, and Vitya gives an answer before the next question is asked.
a) Prove that Masha can always determine Vitya's numbers.
b) What is the least number of questions Masha need to do this for sure, no matter what numbers Vitya guessed?
a) Prove that Masha can always determine Vitya's numbers.
b) What is the least number of questions Masha need to do this for sure, no matter what numbers Vitya guessed?