Daily Math Puzzle: 2026-06-15
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2026-06-15
Dr. Aris is experimenting with three unlabeled vials, A, B, and C. He knows one contains a potent Growth Serum, one contains a Growth Inhibitor, and the third contains Pure Water. He knows: 1. Applying Growth Serum alone makes a plant grow taller. 2. Applying Growth Inhibitor alone makes a plant shrink. 3. Applying Pure Water alone has no effect on a plant's height. 4. When Growth Serum and Growth Inhibitor are mixed, their effects cancel out perfectly, resulting in no change in plant height. 5. When Growth Serum and Pure Water are mixed, the plant grows taller. 6. When Growth Inhibitor and Pure Water are mixed, the plant shrinks. Dr. Aris takes a small sample from Vial A and mixes it with a small sample from Vial B. He applies this mixture to a test plant. The plant *grows taller*. Based on this single experiment, which statement *must* be true?
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Solution
Vial C contains the Growth Inhibitor. — The experiment states that mixing Vial A and Vial B caused the plant to grow taller. Let's analyze the given rules for mixtures:
* Growth Serum + Growth Inhibitor = No change
* Growth Inhibitor + Pure Water = Shrinks
* Growth Serum + Pure Water = Grows taller
Since the plant *grew taller*, the mixture of A and B *must* have been a combination of Growth Serum and Pure Water. This is the only combination that results in growth according to the rules.
This means that one of the vials (A or B) contains the Growth Serum, and the other contains Pure Water.
Given that there are three unique vials (A, B, C) containing one Growth Serum, one Growth Inhibitor, and one Pure Water, if A and B collectively contain the Serum and the Water (in some order), then the remaining vial, C, *must* contain the Growth Inhibitor.
Therefore, 'Vial C contains the Growth Inhibitor' is the only statement that *must* be true.
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