1條maths (要給色)

Since the number is 4-digit and > 9000, so the first digit must be 9.
Let the number be 9ABC.

Rounded off to 2 sign. fig.
9A00/11 = 0
=> A = 9.

Rounded off to 3 sign. fig.
99B0/4 = 0
=>B=2,4,6,8

The possible numbers are 992C, 994C, 996C, 998C.
As this is a odd number, C must be 1,3,5,7or 9.

Finally, the number can be divided by 13.
By try and error,
we can make a guess first,
the number is greater than or equal to 9921.
9921/13 ~ 763
764*13=9932
765*13=9945 -----------> This is the correct number.
766*13=9958
767*13=9971
768*13=9984

9950 / 4 = 2487.5

First, the number must be within the region 9001 - 9999.

Consider the case after rounded off to 2 significant figures. The number is divisible by 11, so only 9900 fulfill the requirement.

i.e. the original number is in 9850 - 9949.

Within such range, odd number divisible by 13 are:
9867, 9893, 9919 and 9945

After rounded off to 3 significant figure, they become:
9870, 9890, 9920 and 9950.

Among them, only 9920 is divisible by 4.

So the number required is 9919.


2007-08-19 15:10:11 補充：
To find the odd number divisible by 13, first divide 9850 by 13.We obtain 757.xxxxxxxxx ...As only odd number need to be considered, add 2 from 757 and multiply it by 13.Continue the steps until the product is greater than 9949.