14. There are 7 empty boxes placed on a circle, numbered $1,2,3,4,5,6,7$ in a clockwise direction. Xiao Ming first places the 1st white chess piece in box 1, then places the 2nd white chess piece in box 3, and the 3rd white chess piece in box 6, ..... After placing the $(\mathrm{k}-1)$-th white chess piece, Xiao Ming counts $(\mathrm{k}-1)$ boxes in a clockwise direction and places the $\mathrm{k}$-th white chess piece in the next box. Xiao Ming places a total of 200 white chess pieces according to this rule. Then, Xiao Qing starts from box 1 and places 300 red chess pieces in these boxes in a counterclockwise direction and according to the same rule. Please answer: How many white chess pieces are in each box? How many chess pieces are in each box?
14. Solution: Number the 7 boxes in a clockwise direction without interruption. The numbers that can be in Box 1 are $1, 8, 15, \ldots, 7k+1$; the numbers that can be in Box 2 are $2, 9, 16, \ldots, 7k+2$; ...; the numbers that can be in Box 7 are $7, 14, 21, \ldots, 7k+7$ (where $k$ is an integer).

According to the rules, Xiao Ming places the 1st chess piece in Box 1, the 2nd chess piece in Box 3, the 3rd chess piece in Box 6, the 4th chess piece in Box 10 (which is Box 3), the 5th chess piece in Box 15 (which is Box 1), the 6th chess piece in Box 21 (which is Box 7), and the 7th chess piece in Box 28 (which is Box 7). Following this pattern, starting from the 8th chess piece, the placement of the chess pieces will repeat, i.e., the 8th chess piece goes into Box 1, the 9th chess piece into Box 3, ..., meaning every 7 chess pieces form a cycle. In this cycle, 2 chess pieces go into Box 1, 2 into Box 3, 2 into Box 7, and 1 into Box 6, while Boxes 2, 4, and 5 do not receive any chess pieces. The number of white pieces in each box is as follows:
$200 = 7 \times 28 + 4$, after 28 cycles, the 197th chess piece goes into Box 1, the 198th into Box 3, the 199th into Box 6, and the 200th into Box 3.

When Xiao Qing places the pieces in a counterclockwise direction, we number the boxes in a counterclockwise direction as well, and similarly, every 7 chess pieces form a cycle. $300 = 7 \times 42 + 6$, we can determine the number of red pieces in each box as follows:
\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline Box Number & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline White Pieces & 57 & 0 & 58 & 0 & 0 & 29 & 56 \\
\hline Red Pieces & 86 & 85 & 43 & 0 & 0 & 86 & 0 \\
\hline Total Pieces & 143 & 85 & 101 & 0 & 0 & 115 & 56 \\
\hline
\end{tabular}