Puzzleup 2017 (12) Candle Burning Overlaps - 拼圖

題目網址: http://www.puzzleup.com/2017/
http://www.puzzleup.com/2017/puzzle/?12
答題時限: 10月26日７ＰＭ－比賽結束（約12月27日）
加分時限: 10月26日７ＰＭ－10月31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）　　

◆CANDLE BURNING OVERLAPS

Three candles are lighted in a room. How many different possible overlaps of
their burning times are there?

一個房間裡有三根蠟蠋點燃著。試問它們之間重疊的燃燒時間有幾種可能狀況？

If the question were asked for two candles, the answer would be 9.

1. The first candle starts, the second one starts, the first one stops, then
the second one stops.
2. The first candle starts, the second one starts, the second one stops, then
the first one stops.
3. The first candle starts, the second one starts, then they stop at the same
time.
4. Candles start at the same time, the first one stops, then the second one
stops.
5. Candles start at the same time, the second one stops, then the first one
stops.
6. Candles start at the same time, then they stop at the same time.
7. The second candle starts, the first one starts, the second one stops, then
the first one stops.
8. The second candle starts, the first one starts, the first one stops, then
the second one stops.
9. The second candle starts, the first one starts, they stop at the same time.

若問題改問兩根蠟蠋，則答案為 9：

1. 蠟蠋１點燃→蠟蠋２點燃→蠟蠋１熄滅→蠟蠋２熄滅
2. 蠟蠋１點燃→蠟蠋２點燃→蠟蠋２熄滅→蠟蠋１熄滅
3. 蠟蠋１點燃→蠟蠋２點燃→蠟蠋１２同時熄滅
4. 蠟蠋１２同時點燃→蠟蠋１熄滅→蠟蠋２熄滅
5. 蠟蠋１２同時點燃→蠟蠋２熄滅→蠟蠋１熄滅
6. 蠟蠋１２同時點燃→蠟蠋１２同時熄滅
7. 蠟蠋２點燃→蠟蠋１點燃→蠟蠋２熄滅→蠟蠋１熄滅
8. 蠟蠋２點燃→蠟蠋１點燃→蠟蠋１熄滅→蠟蠋２熄滅
9. 蠟蠋２點燃→蠟蠋１點燃→蠟蠋１２同時熄滅

Notes:
* For a situation to be considered as an overlap, the burning of each candle
must overlap the burning of at least one other candle.
* The duration between two non-overlapping burning periods is unimportant.
For example, the two cases below are considered the same. (The third candle
ignored for brevity)
1. The first candle starts burning, the second one starts as soon as the
first one stops, then the second one stops.
2. The first candle starts burning, it stops, the second one starts after a
while, then the second one stops.

註：
* 一個狀況要被考慮為有重疊，每根蠟蠋要至少和其他一根蠟蠋的燃燒時間重疊。
* 沒有重疊的燃燒階段之間的時間長短不重要。
例如以下兩種狀況視為相同：(暫時忽略第三根蠟蠋)
1. 蠟蠋１點燃→蠟蠋１熄滅時蠟蠋２立刻點燃→蠟蠋２熄滅
2. 蠟蠋１點燃→蠟蠋１熄滅→一會兒後蠟蠋２點燃→蠟蠋２熄滅

====
感覺這註解有點微妙...

--
將很小又單純的命令《Code》組合成函數《Function》。函數累積成更大更方便的元件《
Parts》，成為程式《App》。接著進行動態結合，相互通訊，打造出服務《Service》。
李奧納多知道，要得到結果，就必須持續進行非常單純的作業。為了展現出匹敵巨大建築
的技術，現在非得將面前的碎片組合起來。
知道這條路多麼遙遠的人，叫做極客《Geek》。
將這份尊貴具體呈現的人，叫做駭客《Hacker》。 －－記錄的地平線 Vol.9 p.299

--