Question 53377
I think this is a really neat problem.  Let x = number of tiles purchased.  Then the total cost of the tiles would be 28x, which must be the same digit repeating.  The total cost will be 
28x = k, or 28x = kk, or 28x = kkk, or 28x = kkkk, etc.


Therefore, you must find a number, such that 
x = k/28, or kk/28, or kkk/28, or kkkk/28, etc.


This can also be written as 
{{{x= k/(4*7)}}} or {{{x= kk/(4*7) }}} or {{{x= kkk/(4*7) }}} or {{{x= kkkk/(4*7) }}} etc.


The problem then is to find a number with repeating digits that is evenly divisible by 7 and 4.  Moreover, since the number must also be divisible by 4, it means that the value of k must be 4 times the number 1 or 11 or 111 or 1111, where you are looking for the smallest such number that is divisible by 7.  


So try dividing 11/7, which does not go evenly.

Try 111/7, which does not go evenly.
Likewise continue with, 1111/7, 11111/7, 111111/7, etc. until you find a number that is divisible by 7.  The latter {{{111111/7= 15873}}} divides evenly.  


The solution to the problem is 15873 tiles, whose cost is 15873*28 = 444444.


R^2 at SCC