HMMT 十一月 2011 · 冲刺赛 · 第 5 题

英文解析

5. [ 6 ] Charlie folds an -inch by 11-inch piece of paper in half twice, each time along a straight lineparallel to one of the paper’s edges. What is the smallest possible perimeter of the piece after two such 2
   folds?
   Answer: Note that a piece of paper is folded in half, one pair of opposite sides is preserved 39
   and the other pair is halved. Hence, the net effect on the perimeter is to decrease it by one of the side 2
   ( )
   lengths. Hence, the original perimeter is 2 + 2 · 11 = 39 and by considering the cases of folding 17
   twice along one edge or folding once along each edge, one can see that this perimeter can be decreased 2
   17 39 39
   by at most 11 + = . Hence, the minimal perimeter is .
   2 2 2