Question 7
A collection of $n$ cards is numbered from $1$ to $n$. Each card has either $1$ or $-1$ on the back. You are allowed to ask for the product of the numbers on the back of any three cards. What is the smallest number of questions which will allow you to determine the numbers on the backs of all the cards if $n$ is (1) $30$, (2) $31$, (3) $32$? If $50$ cards are arranged in a circle and you are only allowed to ask for the product of the numbers on the backs of three adjacent cards, how many questions are needed to determine the product of the numbers on the backs of all $50$ cards?