Expert: Scott A Wilson - 10/19/2009

Question
Help please. Problem = A five digit number with 5 different digits. Place a 2 in front of number to make it a six-digit number.
Multiply the six-digit number by 16. The answer is a seven digit number that begins with the original five-digit number, followed by a 2 and then 0. What is the original five-digit number?

Thanks for help.

Answer
I thought about how to do this, and then decided to let the computer figure it out.
I wrote a quick little program in C++ to do this.  It is given:

#include <stdio.h>
// Take a five digit number, put a 2 in front, multiply by 16, begins with first five digits
// k is the number xxxxx
// n=(200000+k)
// while (n>9999999) n=n/10
// if n=k, put n

void main() {  
 long int k;  // number used
 long int b;  // base multiplier
 long int r;  // result of bk*16

 printf ("This program finds a number such that when 200,000 is added to it and\n");
 printf ("the number is multiplied by 16, the first five digits of the answer\n");
 printf ("are the original number.\n\n");

 k = 10000;   //  k is at least five digits
 while (k<=99999) {
   r = 16*(200000+k);
   if (r/100 == k)   printf ("And the numbers are %ld %ld", k, r);
   k = k + 1;
  }
}
Output: 38095 3809520
The last line is the number and the number n and then 16(200000+n).