[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).

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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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。

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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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。