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?

A total of 115 boxes.  Ten scenarios:

   Lg       Md       Total Total
Lg empty Md empty Sm empty boxes
11  9    16   5   88  102   115
11  8    24  14   80  102   115
11  7    32  23   72  102   115
11  6    40  32   64  102   115
11  5    48  41   56  102   115
11  4    56  50   48  102   115
11  3    64  59   40  102   115
11  2    72  68   32  102   115
11  1    80  77   24  102   115
11  0    88  86   16  102   115

But since at least some of the large boxes must be left empty, the last scenario is invalid.

Edited on January 26, 2009, 12:54 pm

Posted by Sing4TheDay on 2009-01-26 12:41:29