题目网址: https://www.puzzleup.com/2022/ https://www.puzzleup.com/2022/puzzle/?11 答题时限: 12月29日７ＰＭ－比赛结束（约１月13日） 加分时限: 12月29日７ＰＭ－１月４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 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. 将大小一样，颜色不同的两个圆形，随机置於电脑萤幕上。 这些圆形之间会有四种状态： 1. 两圆未接触。 2. 两圆互切，也就是交会於一点。 3. 两圆重叠，前者在上。 4. 两圆重叠，後者在上。 问若有不同色三圆时，会有几种不同的状态？ 注： ．三个圆形应都出现在萤幕上，且只考虑二维。 ．圆形之间具有良序性质(上／下)，例如，首圆在次圆之上，次圆又在三圆之上， 则三圆不可在首圆之上。 https://www.puzzleup.com/2022/img/puzzle/2022/04s.jpg https://www.puzzleup.com/2022/img/puzzle/2022/11s.jpg 相同状态的例子 (译注：这个图理清了之前的争议， 不用考虑三圆间有没有空隙存在， 交叠处被另一圆挡住就直接视作没接触) --

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