When to use overlap

A clue that has overlap must pertain to that single clue. The body of the 12 clue you have in the 1st row of your example and the body of the 16 clue you have in the 2nd row of your example cannot share the same space. Though it may look like overlap it is not. The only overlap you can be certain of, if you're working row is indeed 45 units in length, is the two-square set of the 3rd row of your example. It would be part of the 16 clue.

Here is an approach to figuring out if any overlap will occur in a row/column. It may seem a little complicated but it makes logical sense if you think about it:

First determine the number of squares in any given row/column. Let's take your example. The row is a maximum length of 45 squares/units. Next determine the grand total of the clue values added up, plus one for every clue within the row/column, and finally minus one. The plus one for every clue only works for single color puzzles (color and background) because there must be a minimum space of one between clues as this is a fundemental rule. The minus one acts as an offset because there will always be one less required background per clues in a row/column. So 1+12+16=29, +3 is 32, -1 is 31. So you have 31 squares within a row of 45 that must contain the 29 clue sets and at least 2 background clues.

Now this may seem like a tricky part. 14 of those squares have questionable placement (45-31). If there is a clue within a row/column larger than this number, a part of it can and must be placed. Because you have one clue that is larger than 14, it will have a small portion of its clue placed, i.e. the two squares that I mentioned earlier (16-14). This is all you can ascertain for now that belongs. These two squares represent the most extreme point of the 16 clue if the rest of it were to be placed to the right of those two clues, or to the left.

As an additional example, if you have a row of 10 and a 1 clue, you would end up with 9 uncertain spaces. Of course you know there is no way to know where that 1 clue goes. If you have a 9 clue in a row of 10 spaces, 9+1-1=9 -1=8. This means you have 8 overlapping squares of the 9 clue that you may place and 1 square on either side of the 8 squares must be blank.

Hopefully I've made some sense and helped you understand better. Happy solving

I see what you're saying, Cosmictrombonis, but the "-1" termanology can get somebody confused.

I just think of it differently: Add up the total of the clues +1 between each clue.

Therefore, in the above example:

1
+1 (space between clues)
12
+1 (space between clues)
16
--------------------------------------
31



The same overlap rule works with puzzles of multiple colors, but you have to be careful of the size of each color to see where that overlap might fall. For example, if the 1 & 16 clues were red & the 12 green, you could easily see that only 2 of those 16 red would overlap.