Posted: Mon Aug 23, 2004 7:57 pm    Post subject: 計和~~~唔該幫幫手~

設 的各位數字之和為 A , 而 A 的各位數字之和為 B , 求 B 的各位數字之和 C

請用中文詳盡地解釋~

Posted: Wed Aug 25, 2004 7:50 pm    Post subject: Re: 計和~~~唔該幫幫手~

解這題的關鍵是發現到 C 的數值其實很小。由於 ， 在十進制中的位數是 16211，所以 。A 的數值已經比原來的 細了很多。再取數字和，，已經變成兩個位以內的數。再取一次數字和，不難知道。另一方面，由於 ，所以 C = 7。_________________

世上沒有完美的人完美的事，而我們的責任就是要令自己的表演達至最精彩最完美。所以魔術一直都沒有停頓下來，與時代一起進步去追求無止境的完美。

Posted: Thu Aug 26, 2004 11:11 am    Post subject: 計和~~~唔該幫幫手~

我唔明點解會得出，

，
這幾步～

Posted: Thu Aug 26, 2004 6:31 pm    Post subject:

因為 在十進制中有 16211 個位，每個位都係 0 至 9，所以 的數字和不會大於 的數字和，即是說 。_________________

世上沒有完美的人完美的事，而我們的責任就是要令自己的表演達至最精彩最完美。所以魔術一直都沒有停頓下來，與時代一起進步去追求無止境的完美。

Posted: Thu Aug 26, 2004 10:33 pm    Post subject:

Just a note to help cs55555 understand.

We consider because it can tell us the number of digits of an integer in decimal form. Like in this question, we have . Hence has actually 16210 digits. Finally, to see the conclusion made by Carto, note that considering an integer mod 9 is equivalent to considering the sum of its digits mod 9.

[Edited by Andy. The LaTeX content 4444^4444 was changed to 4444^{4444} so that the exponent 4444 is correctly displayed as it should be. If you think this change is inappropriate, please feel free to tell me. Thanks.]

_________________Sometimes Truth is meanlingless;What means is how you believe in.

偶爾，真相並沒有意義；意義在於你怎樣相信。

Posted: Fri Aug 27, 2004 9:51 am    Post subject:

thanks

Posted: Mon Aug 30, 2004 4:09 pm    Post subject:

我都係睇唔明呀．．．

咁點解C 唔係12 而係 7 既….

我唔明最後mod 9 用黎做乜野呀…

_________________

I am a Form 7 Student in Hong Kong.

Posted: Mon Aug 30, 2004 4:44 pm    Post subject:

正如Milton所說，

任何一個正整數均可唯一寫成，其中()為小於10的非負整數，且。
換言之，的十進制表示是。（例如。）
可以證明，被9除時所得的餘數，與的數位和（）被9除時所得的餘數相等。 所以雖然經過多次轉換（求數字和），但是轉換後的數被9除時所得的餘數恆不改變。

由於，且被9除時餘數為7，所以必為7。

_________________

Therefore do not worry about tomorrow, for tomorrow will worry about itself. Each day has enough trouble of its own.

Posted: Mon Aug 30, 2004 7:17 pm    Post subject:

明白啦..
但係點知 4+4+4+4 mod 9 = 7 4444次方唔駛理~?_________________

I am a Form 7 Student in Hong Kong.

Posted: Mon Aug 30, 2004 7:28 pm    Post subject:

~

(Problem: Prove ?)

(*Maybe* n-1 should be replaced with ; I haven’t investigated this very much)

Posted: Mon Aug 30, 2004 8:27 pm    Post subject:

it should be
also, when u use Euler Thm, u should check that , or equivalently

Posted: Tue Aug 31, 2004 1:41 am    Post subject:

OH thanks a lot 但我未學過.. pure會唔會教架~~??_________________

I am a Form 7 Student in Hong Kong.

Posted: Tue Aug 31, 2004 11:13 am    Post subject:

根據2005年個課程: 唔會. 香港D中學課程好似除左 Prime factorization 同 GCD (=HCF)、LCM 之外冇乜講 number theory…

Posted: Tue Aug 31, 2004 12:02 pm    Post subject:

OH i see le… 我algebra好過calculus好多.. calculus d locus搞到我好亂…. algebra差complex number同埋limit未教… 所以我都做左d past paper嚕~

但係paper 2 一份都未操過~

_________________

I am a Form 7 Student in Hong Kong.

Posted: Mon Mar 21, 2005 5:08 pm    Post subject:

我連卑個mod字班中六都唔識破!!!_________________

A strange F.3 student