Welcome to the Mathematics × Programming Competition #2
歡迎參加數學 × 程式編寫比賽 (第二回)
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。
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!
this is really great!
Hi again, I know your are an expert in programming, I have some interesting ideas about steemit, find me in steemit.chat :)!!
oh I am not really a programming expert... I just know the basic stuffs
Anyway sure I will drop you a message on steemit.chat then :)
Thx!!
Beautiful. I´ll try to find the time to take part. I can try it using Mathematica, and I also could try with pencil and paper. Thanks for these great contests.
thanks for your participation! yes you can use whatever tools to solve it, this is the special part of this contest, though you are additionally rewarded if you choose to use a pure mathematical approach without use of calculators . Enjoy the question! :)
20年前的我應該會做，現在的我...😭😭😭
I have an idea but cannot organize the answer!!!!!
don't give up! add oil XD
Just a gentle reminder guys, remember to upvote this post and the announcement posts (either the chinese one or the english one) in order to be eligible for the competition! And resteem it to get 400% higher chance to win! :)
Very good! upvoted!
!-=o0o=-!
To follow curated math content follow @math-trail.
If you wish @math-trail to follow you then read this article.
It seems to be a very difficult question. But when you got the point, it can be very easy.
Wish my answer is correct haha
I got it now haha ^^
ya when you got it, it is easy! I will take a look at the submitted answer later, hope you got it correct :)
Very nice question. Thanks. I'll keep my mouth shut about hints!!
pm me for hints:)
joking XD
lol have you found out the answer by yourself yet?
Hmm I think yes now lol
thanks! your questions are fun as well, but i don't know how to solve them :(
本身是數學白痴，只用左自己諗法推敲一個答案。希望答得對😂
有時候可能直覺給出的答案就已經是對了呢 哈哈
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城会玩
你們比較會玩啦^^
I took one look at this and wanted to cry.
I hate maths :(
oh dun cry, maths is lovely <3
Submitted!
great, thanks for your participation!
Hope I'm not too late to the party.
No you are never too late, you can still get the 2nd prize if you cannot make it to be the first correct answer!
Damn! I submitted my answer on the post hahaha! I never read the whole rules. I quickly jumped into answering and posting it. LOL
oh ye, it's fine :) remember to continue joining this competition!
p.s. remember not to disclose the answer again though ;)
Is my answer correct? lol :)
it is too difficult for me now!
maybe I could solve it when I was studying pure math..
oh ye sometimes the math knowledge will start to get rusted if you haven't done maths for long time haha
so it's time to sharpen your skills through my challenges here again :)
I have just submitted a numerical answer, and then submitted a second time with a proof and a corrected numerical answer. I'm crossing my fingers !
Great! I will announce the winners probably on Monday :)
Good idea :)
Fun challenge
Upvoted both posts.
Submitted numerical answer.
Resteemed.
Then submitted proof, but also had to resubmit the numerical answer again which was the same as the first time.
Also unable to paste a document or jpeg with a more complete proof and unable to get the math summation symbol, all this modern computer coding jargin is harder than the math. ;)
Looking forward to more challenges.
yes I understand that it maybe difficult to type math equations in Google form... it's not so convenient that photo uploads are not allowed. I will try to think of other better ways to handle this, thanks for your suggestion!
Thanks.
It's ironic that mathematicians and engineers invented computers and now make it difficult to write math equations on. I guess there's not enough money in math even though high tech wouldn't exist without the math of physics, engineering and chemistry.
I guess maybe next time you can try to upload your picture which contains the math equations to sth like imgur.com
and then attach the link in Google form. see if this works for you :)
Thanks. Maybe that will work for me.
I think maybe markdown language could also work, if I can figure out markdown.
On my latest steemit post "Win SBD in this Math Contest..." I couldn't get markdown to work the way I wanted for some equations so you can see where I made 3 lines on paint and saved as a jpeg then loaded it into steemit's post form. It appears that there are several versions of markdown.
Math sure is a lot more fun than trying to figure out computer languages.
ye, just took a look at your math challenge. embedding photos is one of the best way to show math equations, as HTML can't support such complicated markup .