Let N be a non-zero natural number composed of n digits.
Let us then both prepend and append the number 4 to create two new numbers, 4N and N4, that are both (n+1) digits long.
For example, if N is 123, then we create two numbers: 4123 and 1234.
The question is to find the smallest value of N, such that the following equation holds true:
4N = 4*N4
Again, using the example above, this would require that 4123 = 4*1234.
This is obviously not true, so N=123 is not a solution.

So, find the smallest value of N and its length n.


Bonus:
A generalized question: For which values of K can we find a value
of N (of length n) that solves the general equation KN = K*NK, as defined above?


source: March issue of Science 2.0

The problem requires that 4*10^n + N = 4*(10N + 4)

Posted by Steve Herman on 2013-07-18 01:07:35