Welcome to the Mathematics × Programming Competition #2

歡迎參加數學 × 程式編寫比賽 (第二回)

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Question 問題

A regular 2017999-sided polygon is drawn on a rectangular coordinate plane, with (0,0) as its center and the distance between any vertex to the center is 1. It is given that one of the vertices is (1,0). Find the sum of x- and y-coordinates of all the other 2017998 vertices. 在直角坐標系統上，我們以(0,0)為中心畫出一個正2017999邊形。它中心與任意一個頂點的距離為1。已知其中一個頂點為 (1,0)，求其他所有2017998個頂點的x坐標及y坐標之和。 https://ds055uzetaobb.cloudfront.net/image_optimizer/67dbe96a1c538dc2f6ff1e92ae3c928bb0f9b3cd.png Photo source: https://ds055uzetaobb.cloudfront.net/ **Hints**: This question has a short, beautiful and elegant mathematical proof which does not require a calculator at all! However the proof is hard. You may want to focus on solving the problem by programming (brute force), which is much simpler. At least you can get the 'numerical answer' prize right? ;) **提示**: 此題目可用數學方法簡潔地給出證明，而且不需使用計算機！但是要想出證明並不簡單。你或者可以選擇用編程來「暴力」解決問題，這應該會較為簡單。至少你可以得到「數字答案」獎吧? ;) ---

Answer submission 答案提交

- Please submit through this link. - A mathematical proof is not a must, but numerical answer is a must. - This competition will last for 24 hours. After that no more submission would be accepted.
- 請經此連結提交答案。 - 你不一定要提交數學證明，但必須提交數字答案。 - 此比賽將進行24小時，其後將不會再接受新答案。 ---

Rules 規則

- Participants who submit the answer as a comment below this post will be **disqualified**. - Participants can submit for unlimited number of times, however only the latest answer will be considered. - You have to upvote this post AND the announcement post in order to be eligible for the competition.
- 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此帖以及預告帖方能參加比賽。 ---

Prizes 獎品

- The final SBD payout of the English announcement post and the Chinese announcement post would together form the prize pool. - The **first** participant who gave the correct **mathematical proof** will get **25%** of the prize pool. 5 other participants who attempted to provide the proof (do not try to write some trash though, I will exclude you from the lucky draw) will be randomly drawn and each of them will get **5%** of the prize pool. - The **first** participant who gave the correct **numerical answer** will get **25%** of the prize pool. 5 other participants who answered correctly will be randomly drawn and each of them will get **5%** of the prize pool. - Those who resteemed this post or the announcement post will have 400% higher chance to win! - It is possible to win in both the **mathematical proof** award and **numerical answer** award! - If not all prizes are given out, they will be accumulated for the next competition. - @kenchung reserve all the rights to disqualify any suspected cheating players and decide the distribution of prize among the winner(s).
- 英文預告帖及中文預告帖所獲的SBD獎勵將會用作是次比賽的獎池。 - **最快**給出正確**數學證明**的參賽者將獲得獎池的**25％**。其他曾嘗試提供數學證明的參與者之中將隨機抽出5名，他們每人可獲**5％**的獎池。（切勿嘗試提交廢文，否則你的抽獎資格會被取消） - **最快**給出正確**數字答案**的參賽者將獲得獎池的**25％**。其他提交了正確數字答案的參與者之中將隨機抽出5名，他們每人可獲**5％**的獎池。 - Resteem此帖文或預告帖者將有額外400％的得獎機會！ - 你可以同時在**數學證明**和**數字答案**中獲獎！ - 若有獎金未被發放，將累積至下一次比賽的獎池。 - 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。 ---- Upvote, resteem and follow me at @kenchung if you like my posts!