In a small village known as Spectropolis, every person wears corrective lenses (monocles or glasses) that are either clear or tinted.
Half the people wear monocles and half of the remaining people do not wear tinted lenses.
Also, half of the monocle wearers do not wear tinted lenses.
If eighteen tinted lenses are enough to exactly supply the needs of the people in Spectropolis, what is the village's population?
Hint: Try to draw a picture to represent both the full situation and the individual clues.
Also, will guess-and-check work?
Solution Commentary: Rather than a solution, some more questions:
- What fraction of the population wears tinted lenses?
- What fraction of the population wears tinted monocles?
- Why is 3 a magical number in this problem?