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?

(In reply to Analytic Solution by Charlie)

This is the basic idea. She leaves some boxes empty (net gain 0 empty boxes) and she fills some boxes with 8 smaller boxes (net gain: 7 empty boxes)

Since at the end there are 91 more empty boxes than what she started with, she must have added boxes 91/7=13 times. The boxes were added in groups of 8, so there are 13*8+11=115 boxes.

Posted by Gamer on 2009-01-27 03:13:09