title: Maximum N digit number we can make with certain number of match sticks
body: <p><a href="https://i.stack.imgur.com/8jNMG.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/8jNMG.png" alt="enter image description here"></a></p>
  
  <p>The picture shows how many sticks you need to draw each of the digits.
  given a number that consists of N digits. I want to move some sticks to maximize the number. I am not allowed to change the number of digits. It had to have N digits always.I cant remove any matchstick either.</p>
  
  <p>Example:</p>
  
  <pre><code>given 512
  answer:977
  given 079
  answer:997
  </code></pre>
  
  <p>My solution was to count the number of matchsticks we can use. Then we start placing 9 till we run out of it. Then when we encounter that we have problem like one match stick remaining we backtrack and make a different choice for the numbers. I am not sure whether this captures all the cases.
  Is there any flaw in my logic. If so what is a better way?</p>