Knights, Damsels, and Liars

Logic Level 2

Knights always tell the truth. Damsels tell the truth first then lies in the next question (Damsels repeat this procedure). And liars lie. In here, I asked a group of 30 persons.

  • Are you a knight? 30 people answered yes.
  • Are you a damsel? 20 people answered yes.
  • Are you a liar? 10 people answered yes.

How many knights are there in the group?


The answer is 10.

I changed My Name. by I changed my name. , 15, Canada

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2 solutions

Vedant Saini
Mar 24, 2019

The 3rd statement is unnecessary for this problem.

When asked the first question, 

    the knights will answer yes

    the liars will also answer yes (they should answer no but because they lie, they answer yes)

    and the damsels also answer yes (because there 30 people in total and all of them say yes)

When asked the second question, 

    the knights will say no

    the liars will say yes (they should answer no but because they lie, they answer yes)

    the damsels will also say yes (they lied the first time, so they will tell the truth now)

Therefore the people who answered no to the second question were knights so their were 30 − 20 = 10 30 - 20 = \boxed{10} knights altogether.

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The 3rd statement tells me that there are 10 damsels.

I changed my name. - 2 years, 2 months ago

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But the question is asking for the number of knights not damsels.

Vedant Saini - 2 years, 2 months ago

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I know, but in your solution, how did you get 30 - 20 = 10?

I changed my name. - 2 years, 2 months ago

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@I changed My Name. – There are 30 people altogether and there 20 liars and damsels (liars and damsels answered yes to the 2nd question and the problem tells us that 20 people answered yes to the question). So the remaining 10 must be the knights.

Vedant Saini - 2 years, 2 months ago
Saya Suka
Mar 18, 2021

All 30 in the group admitted to being a knight, so all the damsels must have started with their lying (with a unanimous "Yes" replies to the "Knight?" queries posed to them) turn in their alternating procedures. Therefore, these damsels would tell the truth next in answering whether they're damsels in addition to the lying knaves. Since Knights would be the only ones who won't say yes to "Damsel?", the answer would be 30 - 20 = 10 Knights.

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