Puzzleup 2022 (4) THREE CIRCLES - 拼圖

Andrew avatar
By Andrew
at 2022-11-10T10:39

Table of Contents


題目網址: https://www.puzzleup.com/2022/
https://www.puzzleup.com/2022/puzzle/?4
答題時限: 11月10日7PM-比賽結束(約12月29日)
加分時限: 11月10日7PM-11月15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:
.三圓均在螢幕上可見,且為二維圖形。
.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

--
Tags: 拼圖

All Comments

Kama avatar
By Kama
at 2022-11-09T19:04
2017年第18題的復刻,當年這題送分去了
Annie avatar
By Annie
at 2022-11-14T01:59
結果還是不知道 https://imgur.com/a/2Ocl8 要算相同情況
Irma avatar
By Irma
at 2022-11-09T19:04
還是不同情況,我目前是跟據 Difficulty: 15.0 % 來推估
Ula avatar
By Ula
at 2022-11-14T01:59
應該沒有我想的這麼複雜,所以用相同情況下去算。
Michael avatar
By Michael
at 2022-11-09T19:04
那下圖是一種,兩種,還是三種呢?
Mason avatar
By Mason
at 2022-11-14T01:59
https://imgur.com/PLPMVWu
Ida avatar
By Ida
at 2022-11-09T19:04
擦掉黑線: https://imgur.com/a/GaqiSgH
Kumar avatar
By Kumar
at 2022-11-14T01:59
我猜註說的二維圖形意思是有看到就有,沒看到就沒有
Necoo avatar
By Necoo
at 2022-11-09T19:04
也就是如果接觸的部分被第三圓遮住就當作沒接觸了
不用考慮第三圓「背面」可能的情形,那已超出二維
Franklin avatar
By Franklin
at 2022-11-14T01:59
大家也想得太複雜xd
從範例給的情況去考慮就好了吧
Noah avatar
By Noah
at 2022-11-09T19:04
謝謝

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at 2022-11-04T10:44
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