我的一个初级解法

Simplify 32x+30=58y+44 to 16x=29y+7, further to 16(x-y)=13y+7
which means the multiple of 16 divided by 13 has a remainder of 7.

For example, 16/13, remainder is 3; 16*2/13, remainder is the same as (3+16)/13, which is 6;
16*3/13, remainder is the same is (6+16)/13, which is 9; and so on.

We have the following table:

x-y	remainder
1	3
2	6
3	9
4	12
5	2
6	5
7	8
8	11
9	1
10	4
11	7
12	10
13	0

When x-y=11, we have 16*11=13y+7, solve for y and have y=13, then x=24.
Therefore, the first number is 32*24+30 = 798

The next value of x-y with remainder 7 is x-y=11+13=24, then y=29, x=53.
The second number is 32*53+30 = 1726.

The third value of x-y with reminder 7 is x-y=24+13=37, then y=45, x=82.
The third number is 32*82+30 = 2654.

The fourth number is 32*111+30, which is greater than 3000, not qualified.

It is also fine if you start directly from the equation 16x=29y+7 and find the remainders of 16x/29.
But in this situation, you need to list a table of length 29 and each step you have to consider
the bigger number 29 (instead of 13), which involves more work.

 

所有跟帖： 

• this is also a good one; ) -ttmum- ♀ (102 bytes) () 04/17/2014 postreply 21:31:25