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Jenny’s boxes nriddle

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Jenny has boxes in three sizes: large, standard, and small. She puts 11 large boxes on a table. She leaves some of these boxes empty, and in all the other boxes, she puts 8 standard boxes. She leaves some of these standard boxes empty, and in all the other standard boxes, she puts 8 (empty) small boxes. Now, 102 of all the boxes on the table are empty.

The question: How many boxes has Jenny used in total?

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SherlockHolmes Expert Asked on 21st September 2018 in Logic Puzzles.
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    • 1 Answer(s)

    115

    Every time she fills a box with 8 smaller boxes the number of empty boxes increases by 7.
    She has 102 empty boxes. Subtract the original 11 large and divide by 7 giving 13.
    13 times she filled an empty box with 8 smaller boxes. So she uses 11 large boxes and 104 (13×8) other boxes (standard or small) giving 115 in total.

    When we assume she fills all 8 standard boxes in a large box with small boxes than we can calculate the number of standard and small boxes used.
    If she fills a large box with 8 standard boxes an each standard box with 8 small boxes she will have 64 empty small boxes.
    If she does that twice she would have 128 small boxes but the total number of empty boxes is 102 so she does it only once.
    In this case she would have used 11 large boxes 64 small boxes and 40 (=115-11-64) standard boxes.

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    CugelTheWise Expert Answered on 21st September 2018.
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