"Your Game Maker game implements a challenge where the player answers a series of “yes/no” questions to select one of eight possible paths through the forest. What is the smallest number of “yes/no” questions needed to guarantee a decision among the eight possible paths? Please explain your answer in detail, and include all formulas and calculations you used to determine your answer."
I'd like some help understanding what this question is asking for and perhaps a path to figure out the answer, don't give me the answer straight up!
Imagine that there's only 1 question. How many paths are there?
Path 1: yes
Path 2: no
So 1 question makes 2 paths.
If there are 2 questions, how many paths are there?
Path 1: yes, yes
Path 2: yes, no
Path 3: no, yes
Path 4: no, no
So 2 questions make 4 paths.
If there are 3 questions, how many paths are there? I'll get it started...
yes, yes, yes
yes, yes, no
yes, no, yes,
yes, no, no
no, yes, yes
. . .
That is not the complete list. Does that help any?
Remember we are given that there are 8 paths; we want to know the minimum number of questions that make 8 paths.