Problem #53 EASY
The Lighthouse Keeper's Bottles
Logic Math Optimization Scenario
Problem Statement
The Story:
Old Fernandez has kept the lighthouse at the tip of the Ratnagiri coast for over thirty years. He is a quiet man who spends his evenings reading, listening to the radio, and drinking exactly one small glass of local cashew feni before bed.
He gets a supply boat once every six months. On his last delivery, the young supply officer made a clerical error and sent Fernandez 12 bottles of feni instead of the usual six.
Fernandez immediately noticed something was wrong. He lined all 12 bottles up on his shelf and stared at them carefully. Eleven of the bottles were his regular brand — he could tell by the slight cloudiness of the liquid and the weight of the bottle. But one bottle looked and felt identical to the others on the outside, yet he suspected it was a counterfeit filled with a lighter, watered-down liquid.
The supply boat was already heading back to shore. Fernandez had only one tool available — a simple balance scale that sat in the corner of the lighthouse storage room, used for weighing fish catches. The scale had two pans but no weights.
He needed to find the counterfeit bottle in the fewest number of weighings possible.
The Challenge:
Fernandez has 12 bottles, one of which is lighter than the rest. Using a balance scale with no weights, what is the minimum number of weighings needed to guarantee identifying the lighter bottle?
Answer & Quick Explanation
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