MathDB

189

Part of 1974 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 189 All Soviet Union MO 1974 triples of cards with -1 or +1, product

Source:

7/4/2019
Given some cards with either "āˆ’1-1" or "+1+1" written on the opposite side. You are allowed to choose a triple of cards and ask about the product of the three numbers on the cards. What is the minimal number of questions allowing to determine all the numbers on the cards ...
a) for 3030 cards,
b) for 3131 cards,
c) for 3232 cards.
(You should prove, that you cannot manage with less questions.)
d) Fifty above mentioned cards are lying along the circumference. You are allowed to ask about the product of three consecutive numbers only. You need to determine the product af all the 5050 numbers. What is the minimal number of questions allowing to determine it?
combinatoricsminimum