| 發布者 | 內容列 | 訪客
|  求救!! |  | 請幫忙解解下列題目:
A three-digit number N leaves remainder 3 when divided by 7, remainder 5 when divided by 11 and remainder 8 when divided by 17. What is the number N? |
| | 2005-10-10 20:57 | | 訪客
| | Re: 求救!! | | N / 7 =? .........3
N / 11 =?...........5
N / 17 =?...........8
請用孫子算法?再想想看! 我也再算........
sam |
| | 2005-10-10 21:50 | | 訪客
| | Re: 求救!! | | 先把11, 17公倍數
11 x 17 = 187, 187/7=26...5 ( 5不是他們要的,而是3)
5 x 2 =10 10/7=1.....3,
所以 11 x 17 x 2 = 374
======================
7, 17公倍數
7 x 17 = 119, 119/11=10...9
9 x 3 = 27, 27/11=2...5,
所以17x 7 x 3 = 357
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11, 7公倍數
11 x 7 = 77, 77/17=4.......9
9 x 16 = 144 , 144/17=8 ....8
所以 7 x 11 x 16= 1232
=======================
1232 + 374 + 357 = 1963
1963 - N的公倍數
所以11x 7x 17= 1309(N的公倍數)
1963-1309=654
所以三位數是654
Ans:654
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不知我寫您看懂否?
sam
|
| | 2005-10-10 22:23 | | 訪客
| | Re: 求救!! | | 辛苦你了! 謝謝 |
| | 2005-10-11 00:01 | | is990101
Just popping in
註冊日: 2002-08-22
發表數: 6
| | Re: 求救!! | | 從另一個角度看題:由３算起加７的倍數:３,10,17,24,31,38----;由５起算加１１的倍數:5,16,27,38--;共同最小數為３８;自３８起加７７的倍數:38,115,192,269,346,423,500,577,654(所求) |
| | 2005-11-28 15:37 |  | 孫文先
Moderator
註冊日: 2002-07-30
發表數: 1094
| | Re: 求救!! | | 提示：請考慮2N+1
_________________
孫文先 敬上
|
| | 2005-12-01 09:56 |  | qqwwee2006
Just can't stay away
註冊日: 2006-02-18
發表數: 79
火星
| | | 2006-02-19 23:06 | |
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