11. 11
11. 【Solution】The originally empty box is no longer empty, and another box has now become an empty box. This indicates that there was a box that only contained one chess piece, which was taken out, causing the box that originally contained one chess piece to become empty. After this box becomes empty, another box needs to take its place. This box originally contained 2 chess pieces. $\qquad$ It is evident that the number of chess pieces in the original boxes were several consecutive natural numbers starting from 1. The sum of these consecutive natural numbers is more than fifty. Since $1+2+3+4+5+6+7+8+9+10=55$. Therefore, there are 11 boxes.
11. Several identical boxes are arranged in a row. Xiao Ming distributed more than fifty identical chess pieces into the boxes, with only one box left empty. Then he went out. Xiao Guang took one chess piece from each of the boxes that had chess pieces and placed them in the empty box, and then rearranged the boxes. When Xiao Ming returned, he carefully examined everything but did not notice that anyone had tampered with the boxes and chess pieces. How many boxes are there?