Re: Math problem: help

[Pham Thi Thanh Hong <smm68490@ait.ac.th>]

On Sun, 16 Mar 1997, Tuan V Nguyen wrote:

> Hello math folks,
> 
>         My son has a math problem, which I can not figure 
> out yet, and I would be grateful for your help. The problem 
> is: 
> 
> "Find the largest seven-digit number (say X), where X is 
> divisible to every digit. Note that the seven digits are 
> unique (no repetition.)"
> 
> 
> 	Thank you in advance for your help.
> 
> 	Tuan 
> 
> 
> 
> 

Hi Tuan,

Maybe because I did not get the whole idea of the problem, so I found its
solution as simple as follows (If it is not reasonable, you could use it
as a reference, OK.) 

---------------
Solution

Because, it is the largest seven - digit number and those digits are
unique, so I can guest it is formed under a down trend as 9876543.

As assumption that it is divisable for each of digit, X must be divisable
for 2 and 5. This makes it has a 0 in the end. The number also must be
divisable to 9 (as the first digit in the series). It will have 1 in the
sixth digit (9+8+7+6+5+1+0=36; this number is divisable for 9).

Thus, X might be 9876510. This number is divisable for 7 as required
conditions. However, it is not divisable for 8. To find out the real
result, we substract a number that divisable for all 2,5,7, and 9 from
this number (630). This step will be repeated till the remain is
divisable for 8 and sequence of number satisfies the assumption of
different digit composed X.

Following this, we get a solution of 9874620

H