[Question] Mathematics × Programming Competition #7 [問題] 數學 × 程式編寫比賽 (第七回)

Mathematics × Programming Competition #7

^{Designed by @nicolemoker}

21/9/2017 UTC 04:00 - 28/9/2017 UTC 04:00

For Chinese version please scroll to the bottom. 中文版請見文末。

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Question

A point is chosen randomly in a square. 4 lines are drawn to connect this point with the 4 vertices of this square, such that 4 triangles are formed. Find the probability that all interior angles of the 4 triangles are less than 120°. Give your answer correct to the nearest 3 decimal places.

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Answer submission

Please submit your answer through this link.

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Rules

• This competition will last for 7 days. After that, no more submission will be accepted.
• Participants who submit the answer as a comment below this post will be disqualified.
• Participants can submit an unlimited number of solutions, however only the latest answer will be considered.
• You have to upvote this post in order to be eligible for the competition.

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Prizes

• The three fastest contestants would win the first prize, second prize and third prize respectively.
• Other contestants who gave the correct answer would enter a lucky draw. 5 winners will be drawn.
• Those who resteemed this post will have 400% higher chance to win in the lucky draw.
• @kenchung reserves all the rights to disqualify any suspected cheating players and to decide the distribution of prizes among the winner(s).

where n is the total number of winners in this competition. n = min (number of participants getting the correct answer, 8).

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chat channel. You can also consider joining a private curation trail to further support steemSTEM by asking about it in the chat channel. In order to further promote the use of the chat channel, I will stop announcing the time of next competition via a post. Instead I will announce the time in advance in the chat channel!The steemSTEM project (@steemstem) is a community-supported project aiming to increase the quality and the visibility of STEM (STEM is the acronym for Science, Technology, Engineering and Mathematics) articles on Steemit. Please support steemSTEM by following @steemstem and joining the

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數學 × 程式編寫比賽 (第七回)

^{Designed by @nicolemoker}

21/9/2017 UTC 04:00 - 28/9/2017 UTC 04:00

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問題

在一個正方形內隨機選取一點，並將此點與四個頂點連上直線，從而將正方形分割為四個三角形。求四個三角形之中所有內角均不超過 120° 的概率，答案準確至小數點後 3 位。

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答案提交

請經此連結提交答案。

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規則

• 此比賽為時7天，其後將不會再接受新答案。
• 嚴禁在回覆公開答案，否則將被取消資格。
• 參加者可以重覆提交答案，但比賽終結時只會考慮最後提交的答案。
• 你必須upvote此帖方能參加比賽。

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獎品

• 最快給出正確答案的三名參賽者將分別獲得一等獎、二等獎和三等獎。
• 其他給出正確答案的參賽者將可參與抽獎。5名參賽者將被選出。
• Resteem此帖文者將有額外400％的得獎機會。
• 本人保留一切最終權利，包括但不限於取消任何疑似作弊者的資格並決定獲獎者的獎勵分配。

其中 n 是本比賽中得獎者的總數。n = min (答對人數, 8)。

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