Puzzleup 2013 (19) Picked Number - 拼圖

題目網址: http://www.puzzleup.com/2013/
http://www.puzzleup.com/2013/puzzle/?260

答題時限: 11月28日７ＰＭ－比賽結束（約12月11日）
加分時限: 11月28日７ＰＭ－12月２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）　　

◆Picked Number

A number is picked, and five guesses are made to find this number. The
guesses are written on a paper, and the differences between the guesses and
the picked number (by subtracting the smaller from the bigger) are written on
another paper. Later one number is randomly erased from each paper. As a
result there are 4 numbers on each paper.

Guesses: 27, 32, 44, 45
Differences: 5, 7, 10, 13

If the picked number can be found using these information, what is this
number?

有一個數被選取，然後做了五次對這個數的猜測。
這五個猜測一起寫在一張紙上，
然後在另一張紙上寫下這五個猜測跟被選數之間的差 (固定由大減去小)。
然後兩張紙各任意地抹去了一個數。
於是這兩張紙上各剩下了四個數字，如下：

猜測： 27, 32, 44, 45
差距： 5, 7, 10, 13

由這些資訊試求被選數。

--
'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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