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Formula for discovering series of yes/no problems

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"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!

Mar 23, 2018

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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.

Mar 23, 2018