## [Hints] 2013 Singapore MO (Junior Rd 1) Problem 26

2013 SMO (Junior-Rd1) 26. Given any 4-digit positive integer $x$ not ending in ‘0’, we can reverse the digits to obtain another 4-digit integer $y$. For example if $x$ is 1234 then $y$ is 4321. How many possible 4-digit integers $x$ are there if $y - x = 3177$?

Hint: Write $x$ as $x = \overline{abcd} = 1000a + 100b + 10c + 10d$. What equation must $a,b,c,d$ satisfy?