题目网址: http://www.puzzleup.com/2017/
http://www.puzzleup.com/2017/puzzle/?12
答题时限: 10月26日７ＰＭ－比赛结束（约12月27日）
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◆CANDLE BURNING OVERLAPS
Three candles are lighted in a room. How many different possible overlaps of
their burning times are there?
一个房间里有三根蜡蠋点燃著。试问它们之间重叠的燃烧时间有几种可能状况？
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.
若问题改问两根蜡蠋，则答案为 9：
1. 蜡蠋１点燃→蜡蠋２点燃→蜡蠋１熄灭→蜡蠋２熄灭
2. 蜡蠋１点燃→蜡蠋２点燃→蜡蠋２熄灭→蜡蠋１熄灭
3. 蜡蠋１点燃→蜡蠋２点燃→蜡蠋１２同时熄灭
4. 蜡蠋１２同时点燃→蜡蠋１熄灭→蜡蠋２熄灭
5. 蜡蠋１２同时点燃→蜡蠋２熄灭→蜡蠋１熄灭
6. 蜡蠋１２同时点燃→蜡蠋１２同时熄灭
7. 蜡蠋２点燃→蜡蠋１点燃→蜡蠋２熄灭→蜡蠋１熄灭
8. 蜡蠋２点燃→蜡蠋１点燃→蜡蠋１熄灭→蜡蠋２熄灭
9. 蜡蠋２点燃→蜡蠋１点燃→蜡蠋１２同时熄灭
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.
注：
* 一个状况要被考虑为有重叠，每根蜡蠋要至少和其他一根蜡蠋的燃烧时间重叠。
* 没有重叠的燃烧阶段之间的时间长短不重要。
例如以下两种状况视为相同：(暂时忽略第三根蜡蠋)
1. 蜡蠋１点燃→蜡蠋１熄灭时蜡蠋２立刻点燃→蜡蠋２熄灭
2. 蜡蠋１点燃→蜡蠋１熄灭→一会儿后蜡蠋２点燃→蜡蠋２熄灭
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感觉这注解有点微妙...