請教教我點計

圖片參考：http://i187.photobucket.com/albums/x22/cshung/7007111202698.jpg
　　　　　

2007-11-15 20:59:26 補充：
第五題你個答案的確簡單一點，我使用的是Quadratic Diophantine Equation的通解，這對於任何類似的題目都適用，係一個學一次，用幾多次都得既方法。到於其餘既問題，太簡單我冇寫solution喇。答案其實係同你一模一樣。

2007-11-18 21:49:09 補充：
隨便問吧。

I DO NOT think you need to study university before solving question 5, 8, 9!!! My solution is of 'secondary school' level. I always think that easy solution is better ^_^


[Question 5]

4/m+2/n=17

4/m increase as m decrease, so 4/m is maximum when m=1 (since m must be positive integer, m can't be less than 1)

2/n increase as n decrease, so 2/n is maximum when n=1 (since n must be positive integer, n can't be less than 1)

Similarly for 2/n, it is maximum when n=1

Therefore, 4/m + 2/n < 4/1 + 2/1 = 6

So, if m, n has to be positive integer, 4/m + 2/n cannot be greater than 6

So 4/m + 2/n cannot be equal to 17 if m, n has to be positive integer

Therefore, NO SOLUTION for positive integer m,n can fit the equation.



[Question 8]

Let number of workers be P and total number of stone be S

S = XP + 12
S = 8(P-1) + 7

Equating them,

XP + 12 = 8(P-1) + 7
XP + 12 = 8P - 8 + 7
(X-8)P +13 = 0
P = 13/(8-X)

Note that since both P and X must be integer, there is only one solution for X: X=7

P = 13/(8-7) = 13

Therefore, number of workers is 13



[Question 9]

AB
X BA
-------
3040 ... (*)
114
-------
3154

From (*), integer for answer of BxB is 4. So B can only be 2 or 8 (since 2x2=4 and 8x8=64)

If B=2, ABxBA is maximize when A=9. But 92x29= 2668 < 3154
So B cannot be 2, which means B must be 8

From (8) again, since BxB = 8x8 = 64, therefore AxB = 30 - 6 = 24

8A = 24 which gives A= 3

Therefore, A=3 and B=8 (38x83=3154)

2007-11-16 11:22:16 補充：
Andrew, thanks for your answer. Your method in solving Q5 and Q7 is great. Just want to show some alternative method in solving question 5.^_^