[Question] Mathematics × Programming Competition #8 [問題] 數學 × 程式編寫比賽 (第八回)

Good News!

Thanks to @steemstem , the sponsored prize has been doubled!

Please refer to the "Prizes" section for details.

好消息！

感謝 @steemstem 慷慨支持，贊助金額由是次比賽起增加一倍！

詳見下文"獎品"部分。

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Mathematics × Programming Competition #8

^{Designed by @nicolemoker}

13/10/2017 UTC 15:00 - 20/10/2017 UTC 15:00

For Chinese version please scroll to the bottom. 中文版請見文末。

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Question

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

Note that 159 is displayed as 0159

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.

Note that it is acceptable for the ‘1’ to be displayed on the left hand side

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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Answer submission

Please submit your answer through this link.

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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.

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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).

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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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!

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數學 × 程式編寫比賽 (第八回)

^{Designed by @nicolemoker}

13/10/2017 UTC 15:00 - 20/10/2017 UTC 15:00

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問題

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

注意159顯示為0159

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。

注意'1'顯示在左側亦可接受

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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答案提交

請經此連結提交答案。

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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。

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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。

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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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。