Because two pieces are pulled out at a time and put back 1 piece, 1 piece is missing every time. I touched 1999 times, leaving 200 1- 1999=2 pieces.
There are two ways to touch two pieces at a time from the big box:
(1) touches two pieces of the same color. At this time, take out a black chess piece from the small box and put it in the big box. When the two pieces are black, one piece of black is missing from the big box; When the two pieces are white, there is a black one in the big box.
(2) The two pieces in contact are different colors, that is, one piece is black and the other piece is white. At this time, you should put the white piece back in the big box, and there is a black piece missing in the big box.
To sum up (1)(2), every time you touch it, the total number of black pieces in the big box is either one less or one more, which changes the parity of the number of black pieces. It turns out that there are 1000 black chess in the big box, which is an even number of black chess. Touched 1999 times, that is, changed the parity of 1999 times, leaving an odd number of black chess. Because there are only two pieces left in the big box, and the last two pieces are black and white.
The number of callers is always even.
∴ is an even number.
Simplicity is true. ...