题目网址: http://www.puzzleup.com/2017/
http://www.puzzleup.com/2017/puzzle/?18
答题时限: 12月７日７ＰＭ－比赛结束（约12月27日）
加分时限: 12月７日７ＰＭ－12月12日６：５９ＰＭ
答对可得基本分１００分。答案可上传５次，每改１次答案从基本分扣２０分。
比赛期间内可随时上传答案，加分时限内答对第ｎ天加（６－ｎ）分
另依题目的难易有额外加分（如有８０％的人这题答错，答对者加８０分）
◆THREE CIRCLES
Two circles of the same size and different colors are placed randomly on a
computer screen. These circles can be in one of 6 different states:
1. The circles are not touching.
2. The circles are tangent, i.e. touching at a single point.
3. The circles are overlapping, the first one is on top.
4. The circles are overlapping, the second one is on top.
5. The circles are coincident, the first one is on top.
6. The circles are coincident, the second one is on top.
How many different states are there for 3 circles?
两个相同大小但不同颜色的圆随机画在电脑萤幕画面上。它们之间一共有六种状况:
1. 两圆不接触
2. 两圆相切，即它们在一点接触
3. 两圆有重叠，第一圆在上
4. 两圆有重叠，第二圆在上
5. 两圆重合，第一圆在上
6. 两圆重合，第二圆在上
试问三圆共有几种状况？
Notes:
* If the order of overlapping or coincident circles are different in two
states, those states are considered different, even if they are visually the
same, e.g. because overlapping area is covered by another circle.
* The circles have a well defined order (top/bottom), e.g. if the first
circle is on top of the second and the second circle is on top of the third,
the third circle cannot be on top of the first.
* If two circles are coincident, the third one can be tangent to either both
of them or neither of them.
注:
* 只要重叠或重合的情形有所不同时即视为不同的状况，
即使最后结果看起来是一样的 (例如因为重叠处被第三圆盖住了等等)。
(译注: 举个例子是上面的 3 4 两种状况，然后第三圆盖住重叠区，这样算两种；
又例如三圆完全重合，这里一共有六种，即使看起来只有三种)
* 三个圆之间是有上下顺序关系的，
意即若第一圆在第二圆之上，第二圆在第三圆之上，则第三圆不可能在第一圆之上。
* 若两圆重合，第三圆和两圆相切的状况可以是都相切或都不相切。
(译注: 原文我看起来有点在强调不会只切其中一个)