Puzzleup 2014 (14) Five Points - 拼圖

題目網址: http://www.puzzleup.com/2014/
http://www.puzzleup.com/2014/puzzle/?255

答題時限: 10月30日７ＰＭ－比賽結束（約12月17日）
加分時限: 10月30日７ＰＭ－11月５日６：５９ＰＭ

答對可得基本分１００分。答案可上傳５次，每改１次答案從基本分扣２０分。　
比賽期間內可隨時上傳答案，加分時限內答對第ｎ天加（６－ｎ）分　 　　 　　
另依題目的難易有額外加分（如有８０％的人這題答錯，答對者加８０分）　　

◆Five Points

http://www.puzzleup.com/2014/img/puzzle/2014/14.jpg

You will connect the five points given in the figure (the vertices of regular
pentagon) by drawing straight lines.

-You will visit each of the points exactly one time.
-You won’t lift your pencil from the paper while drawing.
-You can cross over the lines.

How many diferent shapes can be obtained?

Notes:
-Rotations and reflections will be counted seperately.
-A shape can not be counted as a new shape if it is obtained by just
changing the direction of the drawing betwen the two terminal points.

Four of shapes included in the solution are shown below.

你要將如上圖的五點 (形成一個正五邊形) 畫直線段連接起來。

* 你將經過每個點正好一次。
* 連接時筆尖不離開紙面。
* 直線段之間可以交叉。

試問可以得到多少種圖形？

註:
* 旋轉及鏡像分開計算。
* 若僅僅是改變線段畫的方向則不算新圖形。

以下為其中四種圖形：

http://www.puzzleup.com/2014/img/puzzle/2014/14_ek.jpg

--
LPH [acronym]
= Let Program Heal us
-- New Uncyclopedian Dictionary, Minmei Publishing Co.

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