1964年IMO的第5題
Five points are given in the plane. Among the lines that connect these five points, no two coincide and no two are parallel or perpendicular. Through each point we construct an altitude to each of the other lines. What is the maximal number of intersection points of these altitudes (excluding the initial five points)?
我算出的答案是310,但我不知道要如何構造出例子,有人有其他答案嗎?

回應

2010-07-18 21:07
那請問要怎麼構造出例子?因為證明了答案小於或等於310後並不代表答案就是310,還要舉出例子。不過舉出例子後要驗證確實有310個交點應該蠻難的吧!

2010-07-20 20:19
可是他好像也沒有構造例子,只是證明了最大值而已,這種題目應該要構造出例子才可以吧