Bonus problem (Among Us: Find the Imposter)

Logic Level 2

( Note - this is a bonus question to this problem , so if you haven't done that problem, you should first do it and then the bonus problem. )

BONUS PROBLEM - If everybody looked the same(all our blue squares with no accessories or striations), then how many questions do you need to ask to figure out who the imposter is?


The answer is 4.

Aditya Mittal by Aditya Mittal , 14, India

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2 solutions

Vishruth K
Apr 6, 2021

Oof. I thought we had their names, but no, cuz I did it that way. Well, I guessed 4 in the end. I guessed 5, 1, and 4.

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It can be done in that way also, asking if the Imposter's name starts from a or b or c and so on. Using numbers is shorter.

Aditya Mittal - 2 months, 1 week ago

ye ok, i like your solution

Vishruth K - 2 months ago

though if all of the suspects had no accessories, and they would randomly be truthful or not, it's VERY hard.

Vishruth K - 2 months ago

also if they had the same names

Vishruth K - 2 months ago
Aditya Mittal
Apr 6, 2021

The answer is 4.

You just need to ask the right question. If you give them numbers from 1 to 16, you can easily get the Imposter.

The first question could be "is the Imposter's number even or odd?" This question can bring down the number of suspects by 1/2. Now you have only even or odd numbers.

If the imposter is in the odd group, you can ask if the Imposter's number is divisible by 3 or 7 and then you will have only 4 suspects. Then you can randomly make groups of 2 people and ask if it is in one of them. Now you have only two people left and you just have to ask one question to figure out who the imposter is.

If the imposter is in the even group, you can ask if the Imposter's number is divisible by 4 and get the number of suspects to be 4. Then you could ask if the Imposter's number is greater than 9(this question works for both the cases, if the number is divisible by 4 or not). Now you have to ask a single question to figure out the Imposter.

This is just one way of asking questions and naming the people. You can have negative numbers also. And the questions you ask can be anything if it helps you get the answer.

You just have to ask the right question.

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