Determine analytically a positive four digit whole number with no leading zeroes which is such that the value obtained by reversing the number is 81 less than twice the original number.

Still working on the analysis, but the number in question is 3987.

(3987 * 2) - 81  =  7893

Some initial analysis....

Given abcd, where a, b, c, and d are the digits of a positive integer we know that d must be odd {1,3,5,7,9} because (abcd + 81)/2 results in a positive integer.  As 81 is less than 100, we know that a must be odd because dcba is the digits of abcd, but in inverse order.  Because dcba is greater than abcd, the first digit of abcd must be either 1 or 3 and the fourth digit, therefore, must be 9 or 7.  By doubling the number and subtracting 81, it can be seen and concluded that only a number beginning with 3 and ending with 7 could satisfy the given reflective requirement. 

Thus, the number can be seen to fall between 3007 and 3997. 

Edited on December 7, 2006, 6:09 pm

Posted by Dej Mar on 2006-12-07 15:43:23