<h2><center>Mathematics × Programming Competition #7 </center></h2>

https://steemitimages.com/0x0/https://steemitimages.com/DQmb33Qwu5vome8xQ2ZLcqFxZmFwV255hPGovzavXSUDtaX/math%26progLOGO-01-01.png

<center><sup>Designed by @nicolemoker</sup></center>

<h2><center>21/9/2017 UTC 04:00 - 28/9/2017 UTC 04:00</center></h2>

<center><h6>*For Chinese version please scroll to the bottom. 中文版請見文末。*</h6></center>

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<center><h2>Question</h2></center>

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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<h2><center>Answer submission</center></h2>

Please submit your answer through this <a href="https://goo.gl/forms/OXj1Bafe4QOU2c3p2">link</a>. 

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<h2><center>Rules</center></h2>

- 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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<h2><center>Prizes</center></h2>

- 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).

Name of prize | Max no. of prizes | SBD | SP (sponsored by @steemstem ! )
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First prize| 1 | SBD payout of this post / *n* | 7.5
Second prize| 1 | SBD payout of this post / *n* | 5
Third prize| 1 | SBD payout of this post / *n* | 2.5
Consolation prize| 5 | SBD payout of this post / *n* | 0

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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<center>https://steemitimages.com/0x0/https://steemitimages.com/DQmY2jUCgfijKRkYnpsENa1jpv6VFwWe8Ts88cYKcQjiLcp/image.png</center>


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 <a href ="https://steemit.chat/channel/steemSTEM">chat channel</a>. 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! 

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<h2><center>數學 × 程式編寫比賽 (第七回) </center></h2>

https://steemitimages.com/0x0/https://steemitimages.com/DQmb33Qwu5vome8xQ2ZLcqFxZmFwV255hPGovzavXSUDtaX/math%26progLOGO-01-01.png

<center><sup>Designed by @nicolemoker</sup></center>

<h2><center>21/9/2017 UTC 04:00 - 28/9/2017 UTC 04:00</center></h2>

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<center><h2>問題</h2></center>

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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<h2><center>答案提交</center></h2>

請經<a href="https://goo.gl/forms/OXj1Bafe4QOU2c3p2">此連結</a>提交答案。

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<h2><center>規則</center></h2>

- 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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<h2><center>獎品</center></h2>

- 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。

獎項 | 獎項數目 | SBD | SP (由 @steemstem 贊助！)
---|---|---|---
一等獎| 1 | 此帖文的 SBD 金額 / *n* | 7.5
二等獎| 1 | 此帖文的 SBD 金額 / *n* | 5
三等獎| 1 | 此帖文的 SBD 金額 / *n* | 2.5
安慰獎| 5 | 此帖文的 SBD 金額 / *n* | 0

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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<center>https://steemitimages.com/0x0/https://steemitimages.com/DQmY2jUCgfijKRkYnpsENa1jpv6VFwWe8Ts88cYKcQjiLcp/image.png</center>


steemSTEM（@steemstem）是一個由steemit社群支持的項目，旨在宣傳STEM（STEM是科學，技術，工程和數學的首字母縮略詞）。 請追蹤 @steemSTEM 以及加入<a href ="https://steemit.chat/channel/steemSTEM">聊天頻道</a>來支持steemSTEM。你還可以透過加入自動點讚系統來在為了進一步支持steemSTEM，詳情請在聊天頻道內向負責人士查詢。為了推廣聊天頻道的使用，我將不再透過發文來宣布下一場比賽的時間，我會在聊天頻道中提前公佈比賽時間。