A Classic Knights and Knaves problem
A classic goes as follows:
A group of Knights and Knaves work for Ye Ole Beer Shoppe. Knights always tell the truth, while Knaves always lie. When each and every one of the employees were asked two questions, they said the following answers:
"How many people work harder than you?"
At most people work harder than I do.
"How many people get better payment than you?"
At least people have better salaries.
The question to the reader is:
"How many employees worked at Ye Ole Beer Shoppe in total?"
We assume the reader never lies. However, if you do choose to lie, it is to your own discretion as you will get the answer to the question wrong.
Image credit: Wikipedia Piotrus
The answer is 111.
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If we arrange the employees in order of how hard they work, if all of them say the same statement, then the first 1 1 people must be knights. Thus, there are 1 1 knights in all the employees. Now, if we arrange the employees in order of income, the first 1 0 0 people would be lying, whereas anyone after 1 0 0 people would be telling the truth. We know that there are 1 1 such people. Thus, the total number of employees is 1 1 1