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

in contest •  last year

## Good News!

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

Please refer to the "Prizes" section for details.

## Mathematics × Programming Competition #8

Designed by @nicolemoker

## 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?

## 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.

## 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 prizeMax no. of prizesSBDSP (sponsored by @steemstem ! )
First prize1SBD payout of this post / n15
Second prize1SBD payout of this post / n10
Third prize1SBD payout of this post / n5
Consolation prize5SBD payout of this post / n0

where n is the total number of winners in this competition. n = min (number of participants getting the correct answer, 8).

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!

## 數學 × 程式編寫比賽 (第八回)

Designed by @nicolemoker

## 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

## 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。

## 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。

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。

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https://steemit.com/cn/@speeding/one-line-python-math-programming

print(int(sum(map(lambda d: 0.5 if d != ''.join(map(lambda i:'012xx59x86'[int(i)], d[::-1])) and ''.join(map(lambda i:'012xx59x86'[int(i)], d[::-1])) in ['%04d' % x for x in range(0, 10000)] else 1 , ['%04d' % x for x in range(0, 10000)]))))

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submitted, voted and resteeeeeeeeeeeeeeem!

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thanks for joining (again) ! ;)

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Nice! I submitted my answer! 😼

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great! :)

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It seems it's not so late. I decide to reply first to get a nice position:)
Btw, I see there may be a mistake on competition period
"13/10/2017 UTC 15:00 - 20/11/2017 UTC 15:00"
I think it should be:
"13/10/2017 UTC 15:00 - 20/10/2017 UTC 15:00".

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just to remind you that your final position depends on the time of your answer submission through the google form, not the timestamp of your comment here ;)

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Thank you, already summited

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thanks for spotting the mistake, I have just updated it :)

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I'm not able to answer this question but I'll resteem this because it's a good question

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thanks so much!

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sure you can. you can write them all down one at a time, and hope you can identify a pattern (or hope you don't make a counting error). Or, you can learn how to code. This is a simple one through coding.

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Am I late? submitted and resteemed~~

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not quite late i guess, but even if the first 3 spots have been taken, you can still have the chance to get a random prize!

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thanks for joining!

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I hate maths, I'm probably lost here. Let me come and be going 🏃🏃🏃🏃🚶🚶

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sorry to hear that you hate maths, hopefully this question did not make you hate it more! haha

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commenting so I can resteem later, if I remember and am able to.

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great :) thanks for joining

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It won't let me resteem. Timed out the other day. Oh well.

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submitted one day later. Hope my answer is correct and luckily get the prize=]
btw I've use some excel function to do it. Hope my logic is correct haha.

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ye I think it is possible to use Excel to solve this question :) hope that you can win!

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May I use contents of this post in my blog for illustrating the solution?(in the future, not now). I will comment where I quote them from.

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ye sure!

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submitted my answer :)
luckily i saw your announcement 1 hour ago in the steemstem channel, so I can catch your post on time!

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ye if you join the steemstem channel you would know the time of competition in advance!

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waiting to see the answer :) hopefully got it right