Puzzleup 2015 (1) Same Sum - 拼圖

一年一度的 Puzzleup 今天開始～

有關規定可以爬文，主要重點是請避免在公開地方講答案

(直接拿去年第一題的文 repo 了 XD)

題目網址: http://www.puzzleup.com/2015/
http://www.puzzleup.com/2015/puzzle/?1
答題時限: ７月30日７ＰＭ－比賽結束（約12月16日）
加分時限: ７月30日７ＰＭ－８月５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）　　

◆SAME SUM

You randomly select two different 2-digit numbers and calculate their sum.
Your friend does the same operations. What is the probability of you and your
friend having the same sum?

If the problem was asked for two 1-digit numbers, the answer would be 29/405.

Enter your answer as a simplified fraction.

你隨機選取兩個不同的二位數，並計算其和。你的朋友也如此做。
試問你們得到的和相等的機率為何？

若題目改問兩個一位數，則答案為 29/405。

答案請輸入最簡分數。

--
'You've sort of made up for it tonight,' said Harry. 'Getting the
sword. Finishing the Horcrux. Saving my life.'
'That makes me sound a lot cooler then I was,' Ron mumbled.
'Stuff like that always sounds cooler then it really was,' said
Harry. 'I've been trying to tell you that for years.'
-- Harry Potter and the Deathly Hollows, P.308

--