cosmictrombonis:

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.

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.