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Friday, February 29, 2008

The Empty Flask

An apothecary found six flasks capable of holding sixteen, eighteen, twenty-two, twenty-three, twenty-four, and thirty-four fluid ounces respectively. He filled some with distilled water and then filled all but one of the rest with alcohol, nothing that he had used twice as much alcohol as water.
Which flask was left over? And which flasks were used for distilled water, which for alcohol?



SOLUTION :

Since the apothecary had used twice as much alcohol as water, the total ounces of alcohol and water together must be divisible by 3. The total capacity of all 6 flasks is 137 ounces, a number which is 2 more than a multiple of 3. Because the apothecary left one flask empty, it is obvious that this flask must have had a capacity in ounces which is 2 more than a multiple of 3. The only flask which meets this requirement is the one with a capacity of 23 ounces. This flask must have been the one left empty. The remainder, which have a combined capacity of 114 ounces, were filled. One-third of this total, 38 ounces, was water. The 16 and 22-ounces flasks must therefore have been used for water and the 18, 24, and 34-ounce flasks used for alcohol. -QED-

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