Puzzleup 2022 (11) THREE CIRCLES - 拼圖

題目網址: https://www.puzzleup.com/2022/
https://www.puzzleup.com/2022/puzzle/?11
答題時限: 12月29日７ＰＭ－比賽結束（約１月13日）
加分時限: 12月29日７ＰＭ－１月４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）　　

◆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 4 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.

How many different states are there for 3 circles with different colors?

Notes:
*All three circles should be seen on the screen and considered
two-dimensional.
*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.

將大小一樣，顏色不同的兩個圓形，隨機置於電腦螢幕上。
這些圓形之間會有四種狀態：

1. 兩圓未接觸。
2. 兩圓互切，也就是交會於一點。
3. 兩圓重疊，前者在上。
4. 兩圓重疊，後者在上。

問若有不同色三圓時，會有幾種不同的狀態？

註：
．三個圓形應都出現在螢幕上，且只考慮二維。
．圓形之間具有良序性質(上／下)，例如，首圓在次圓之上，次圓又在三圓之上，
則三圓不可在首圓之上。

https://www.puzzleup.com/2022/img/puzzle/2022/04s.jpg

https://www.puzzleup.com/2022/img/puzzle/2022/11s.jpg
相同狀態的例子

(譯註：這個圖理清了之前的爭議，
不用考慮三圓間有沒有空隙存在，
交疊處被另一圓擋住就直接視作沒接觸)

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