title: Algorithm: Determine if a combination of min/max values fall within a given range
body: <p>Imagine you have 3 buckets, but each of them has a hole in it. I'm trying to fill a bath tub. The bath tub has a minimum level of water it needs and a maximum level of water it can contain. By the time you reach the tub with the bucket it is not clear how much water will be in the bucket, but you have a range of possible values.</p>
  
  <p>Is it possible to adequately fill the tub with water?</p>
  
  <p>Pretty much you have 3 ranges (min,max), is there some sum of them that will fall within a 4th range?</p>
  
  <p>For example:
  Bucket 1 : 5-10L
  Bucket 2 : 15-25L
  Bucket 3 : 10-50L</p>
  
  <p>Bathtub 100-150L</p>
  
  <p>Is there some guaranteed combination of 1 2 and 3 that will fill the bathtub within the requisite range? Multiples of each bucket can be used.</p>
  
  <p>EDIT: Now imagine there are 50 different buckets?</p>