<h2><center>Good News!</center></h2>

<h3><center>Thanks to @steemstem , the sponsored prize has been doubled! </center> </h3>

<center>Please refer to the "Prizes" section for details. </center>

<h2><center>好消息！</center></h2>

<h3><center>感謝 @steemstem 慷慨支持，贊助金額由是次比賽起增加一倍！</center> </h3>

<center>詳見下文"獎品"部分。</center>


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<h2><center>Mathematics × Programming Competition #8 </center></h2>

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

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

<h2><center>13/10/2017 UTC 15:00 - 20/10/2017 UTC 15:00</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>

Ken has a four-digit calculator which displays numbers using the seven-segment-display. For example the number 159 is displayed as

<center>https://steemitimages.com/DQmdzSzwdBK2McUY7b1FvoFHWxBxNmshbv1AextGymCLMCq/image.png</center>
<center><h6>Note that 159 is displayed as 0159</h6></center>

Suppose we want to use non-transparent cards to represent all the possible 4-digit numbers from 0000 to 9999. Each card will show one 4-digit number, where the numbers are written using seven-segment-display. However when some cards are rotated 180°, a new number can be formed. For example when the card 0159 is rotated 180°, it becomes 6510.
<center>https://steemitimages.com/DQmeUxm44PWNVixdNomuYDXkEJmBvJCnqZ8oqxorumPUzne/a.png</center>
<center><h6>Note that it is acceptable for the ‘1’ to be displayed on the left hand side</h6></center>

Considering the possibility of rotating a card 180°, what is the minimum number of non-transparent cards required to represent all the possible 4-digit numbers from 0000 to 9999?

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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 ! )
---|---|---|---
First prize| 1 | SBD payout of this post / *n* | 15
Second prize| 1 | SBD payout of this post / *n* | 10
Third prize| 1 | SBD payout of this post / *n* | 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 (第八回) </center></h2>

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

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

<h2><center>13/10/2017 UTC 15:00 - 20/10/2017 UTC 15:00</center></h2>

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<center><h2>問題</h2></center>

Ken有一部只能顯示四位數的計算器，它使用七段顯示來顯示數字。例如，159顯示為

<center>https://steemitimages.com/DQmdzSzwdBK2McUY7b1FvoFHWxBxNmshbv1AextGymCLMCq/image.png</center>
<center><h6>注意159顯示為0159</h6></center>

假設我們要使用非透明卡紙來表示從0000到9999所有可能的4位數字。每張卡紙將顯示一個4位數字，而這些數字是使用七段顯示器所寫成的。留意當某些卡片旋轉180°時，可以形成新的數字。例如當卡片0159旋轉180°時，它將變成6510。
<center>https://steemitimages.com/DQmeUxm44PWNVixdNomuYDXkEJmBvJCnqZ8oqxorumPUzne/a.png</center>
<center><h6>注意'1'顯示在左側亦可接受</h6></center>

考慮到將卡紙旋轉180°的可能性，最少需要多少張卡紙才能表示從0000到9999所有可能的4位數字？

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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* | 15
二等獎| 1 | 此帖文的 SBD 金額 / *n* | 10
三等獎| 1 | 此帖文的 SBD 金額 / *n* | 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。