Truth and lie
In a particular group, some tell the truth, while some lie.
There are 9996 people in a group. One day, the group sat in a circle. Each person in the group said:
"Both the person on my left and right are liars."
What is the difference between the largest and the smallest number of people who could be telling the truth?
The answer is 1666.
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1 solution
For maximum, we select every alternate person. Which is 9996/2 = 4998.
For minimum, we select every third person. Which is 9996/3 = 3332.
So the answer is 4998-3332 = 1666.