Mathematics × Programming Competition #7

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

Answer submission

Please submit your answer through this link. ---

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. ---

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). Name of prize | Max no. of prizes | SBD | SP (sponsored by @steemstem ! ) ---|---|---|--- 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). ---- https://steemitimages.com/0x0/https://steemitimages.com/DQmY2jUCgfijKRkYnpsENa1jpv6VFwWe8Ts88cYKcQjiLcp/image.png 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 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! --- ----

數學 × 程式編寫比賽 (第七回)

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

答案提交

請經此連結提交答案。 ---

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。 ---

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。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)。 --- https://steemitimages.com/0x0/https://steemitimages.com/DQmY2jUCgfijKRkYnpsENa1jpv6VFwWe8Ts88cYKcQjiLcp/image.png 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 以及加入聊天頻道來支持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。