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 Boxed in boxes (Posted on 2009-01-26)
Anne has boxes in three sizes: large, medium, and small.

She puts 11 large boxes on a table. She leaves some of these boxes empty, and in each of the other boxes she puts 8 medium boxes. She leaves some of these medium boxes empty, and in each of the other medium boxes she puts 8 (empty) small boxes. Now, 102 of all the boxes on the table are empty.

How many boxes has Anne used in total?

 See The Solution Submitted by K Sengupta Rating: 4.5000 (2 votes)

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 Analytic Solution | Comment 2 of 3 |

You start with 11 empty boxes.  Boxes are added in groups of 8, all empty to begin with, but filling a previously empty box, for a net gain of 7 in the count of empty boxes.

As there are 102-11=91 more empty boxes now than at the beginning, the process of adding 8 boxes was done 91/7 = 13 times. So there are 11 + 8*13 = 115 boxes now present.

 Posted by Charlie on 2009-01-26 14:40:35

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