Go into an orchard In which there are three gates Thro all of which you must pass Take a certain number of apples To the first gate keeper I give half of that number & half an apple To the second gate keeper I give half of what remain and half an apple To the third gate keeper I give half of what remain and half an apple And yet I never cut one Apple Determine the smallest number of apples Coleridge could start with and fulfill all the stated conditions.
The smallest number of apples has to be 7. To the first gatekeeper Coleridge gives half of 7, that's 3. 5 plus half an apple, that's . 5 to make 4 apples. 7-4 = 3. To the second gate keeper, Coleridge gives half of 3 apples plus half an apple, 1. 5 + . 5 = 2 apples. 3 = 2 = 1 To the third gatekeeper, Coleridge gives half of 1 apple plus half an apple, . 5 plus . 5 = 1.
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