HMMT 十一月 2011 · 冲刺赛 · 第 5 题

HMMT November 2011 — Guts Round — Problem 5

[ 6 ] Charlie folds an -inch by 11-inch piece of paper in half twice, each time along a straight line 2 parallel to one of the paper’s edges. What is the smallest possible perimeter of the piece after two such folds?

解析

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