Puzzleup 2013 (20) Twelve Numbers - 拼圖

題目網址: http://www.puzzleup.com/2013/
http://www.puzzleup.com/2013/puzzle/?261

答題時限: 12月５日７ＰＭ－比賽結束
加分時限: 12月５日７ＰＭ－12月９日６：５９ＰＭ

答對可得基本分１００分。答案可上傳５次，每改１次答案從基本分扣２０分。　
比賽期間內可隨時上傳答案，加分時限內答對第ｎ天加（６－ｎ）分　 　　 　　
另依題目的難易有額外加分（如有８０％的人這題答錯，答對者加８０分）　　

◆Twelve Numbers

There are twelve cards which are numbered from 1 to 12. You shuffle the
cards, and open them one by one. For each card, if the card has a number
larger then all previous cards, you score 1 point. After all the cards are
opened, the sum of the scores is your total score. If you repeat this
operation many times, what would be the average of your total score.

Note: For the first card you score 1 point directly.

(If your answer is not an integer, enter it with two digits after the
decimal point without rounding.)

有十二張牌編號由 1 至 12。你將這些牌洗牌，再將其一一翻開。
若每張牌翻開時它比所有目前已翻開的牌都大，則你得一分。
在所有卡都翻開後，所有分數和就是你的總分。
若重覆這個動作許多次，問總分的平均是多少？

註: 第一張牌翻開時直接獲得一分。
(譯註: 即是說第一張牌比目前是空集合的「所有」已翻開的牌大，故得分)

若答案不是整數，則無條件捨去到小數後第二位。

--
'Oh, Harry, don't you see?' Hermione breathed. 'If she could have done
one thing to make absolutely sure that every single person in this school
will read your interview, it was banning it!'
---'Harry Potter and the order of the phoenix', P513

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