Question

There are 8 boxes. You want to find the box with money in it. How would you find it using the minimum number of binary (Y/N) questions? Calculate the amount of information (in bits)

a) 2 questions, 2 bits.
b) 3 questions, 3 bits.
c) 4 questions, 4 bits.
d) 8 questions, 8 bits.

Answer 1

To find the box with money using the minimum number of binary questions, we can use a binary search algorithm and determine the amount of information in bits needed for different numbers of questions.

Step-by-step explanation:

To find the box with money using the minimum number of binary questions, we can use a binary search algorithm. By asking binary (Y/N) questions, we can narrow down the possibilities with each question. For example, in 2 questions, we can divide the 8 boxes into 4 possibilities each time: 4 boxes, 2 boxes, 1 box. So, we need 2 bits of information. Similarly, with 3 questions, we can divide the boxes into 2 possibilities each time: 4 boxes, 2 boxes, 1 box. So, we need 3 bits of information. This pattern continues for 4 questions and 8 questions, where we need 4 bits and 8 bits of information, respectively.