The NUMBER is 1687392

[Dung Trong Nguyen <nguyen@jaist.ac.jp>]

Pham Thi Thanh Hong <smm68490@ait.ac.th> wrote:

>  Hi Tuan, & Trung
>  
>  Sorry for a wrong previous solution. This number is undivisable for 8. I
> have tried another way to get solution as follows:
>  
>  ---------------
>  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.
>  
> Firstly, we have to find a smalleast number that is divisable for every
> digit. This must be 2520.
> 
> The maximum number that is divisable for 2520 under 9876543 is 9875880.
> Because this number consists of triple 8, therefore, we must to find
> another one which under this value. 
> 
> By subtracting the amount of 2520 from the number of 9875880 till every
> digit of X is different each other, we get the result of 9843120.  
> 
> Thus, the expected number must be 9843120.
>  
> Test it again, OK.

Hi Hong,

I think your number is not divisible to 0.  No number can be.

This is mine (with a little help from my computer :))

1) There no 0, so 9 digits remain.

2) The least sinificant digit can't be odd number. If it is, the
number can not be divisible to 2, 4, 6 and 8 and we don't have enough
number.  Because there no 0 and the least significant digit is event,
there no 5 in our number.

3) 8 number 1,2,3,4,6,7,8 and 9 remain.

4) If there no 9 in the number, 1+2+3+4+6+7+8 = 31, the number can not 
be divisible to 3.

5) If number include 9.  Because 1+2+3+4+6+7+8+9 = 40, there is only
one way to make the 7-digit number be divisible to 9 is excepting 4
from the set of digits.

8) So 7 digits 1,2,3,6,7,8,9 remain to used.

9) 1*2*3*6*7*8*9 = 18144

10) We must check out 496 numbers those have the form (n * 18144) in
the range (>=1016064 and <= 9997344) to get the valid and biggest
number.  That number is 1687392, if the following program is bug-free
:)

d~

--cut here--------------------------------------------------------

#include <stdio.h>

#define MUL (2 * 3 * 6 * 7 * 8 * 9)
#define MAX ((10000000 / MUL) * MUL)
#define MIN ((1000000 / MUL + 1) * MUL)

int a[7];

ten_power(int n)
{
     int i;
     int t;

     t = 1;
     for (i = 0; i < n; i++)
	  t = t * 10;
     return t;
}

digit(int n, int p)
{
     n = n / ten_power(p);
     return n % 10;
}

distinctive(int n)
{
     int i;

     for (i = 0; i < 7; i++)
	  a[i] = 0;

     for (i = 0; i < 7; i++) {
	  int d;
	  int j;

	  d = digit(n, i);
	  if (d >= 1 && d <= 3) {
	       j = d - 1;
	       a[j]++;
	  } else if (d >= 6) {
	       j = d - 3;
	       a[j]++;
	  } else
	       return 0;

	  if (a[j] > 1)
	       return 0;
     }
     return 1;
}

main()
{
     int n;

     n = MAX;
     while (n >= MIN) {
	  if (distinctive(n)) {
	       printf("%d\n", n);
	       exit(0);
	  }
	  n -= MUL;
     }
     printf("no solution\n");
     exit(0);
}

--cut here----------------------------------------------------------