HMMT 二月 2003 · COMB 赛 · 第 6 题

英文解析

6. In a classroom, 34 students are seated in 5 rows of 7 chairs. The place at the center ofthe room is unoccupied. A teacher decides to reassign the seats such that each studentwill occupy a chair adjacent to his/her present one (i.e. move one desk forward, back,
   left or right). In how many ways can this reassignment be made?
   Solution: 0
   Color the chairs red and black in checkerboard fashion, with the center chair black.
   Then all 18 red chairs are initially occupied. Also notice that adjacent chairs have different colors. It follows that we need 18 black chairs to accommodate the reassignment,
   but there are only 17 of them. Thus, the answer is 0.