# blue puzzles third room Rule: blue and yellow dots have to be in the same enclosed area if you need subtraction.

1. Z
ziggurcat

can you perhaps explain what you mean by “blue and yellow dots have to be in the same enclosed area if you need subtraction”? i’m especially looking at the last puzzle in this image, and it makes absolutely zero sense to me how to get to that conclusion.

1. G
Gosu No0b

The point of the puzzles is to outline the shape defined by the yellow dot squares (including the square with the yellow dots inside that outline). Blue dots, on the other hand, can be used to subtract from the shape defined by the yellow dots. The last puzzle for example – bottom yellow dot shape has three little squares in a form of a letter L. But – inside the outline are also two blue dot shapes that together have three little squares. When you subtract three little squares from the yellow shape you get zero and that means the bottom of the puzzle is whatever you want it to be (if the outline consists of both yellow and blue shapes with three little squares each). Same goes for the upper part of the puzzle, because 4 yellow and 4 blue little squares amount to zero. I hope this helps.

1. F
FilthyFur

Oh wow without that explanation, and the fact you are expected to make it 0 squares i would have never been able to solve that o.O

2. R
rbtroj

Sorry to be 10 months late to the party, but I’m just getting around to The Witness now. I still don’t follow the logic here. I get the math: hollow blue subtracts from whatever you have to draw around, but I still don’t get how you determine which shape to outline. In the third puzzle, for instance, why does it have to be the “L” shape? To my mind, the rules should allow me to eliminate the need for all three of those and then with the one remaining blue square from any of the four yellow in the square shape. And for that matter, in the fourth puzzle, if all it is is a matter of “drawing zero” squares, then why doesn’t any random line work. I’m no mathemagenius, but there have been at least a couple of puzzles so far where I’ve satisfied the rules, yet the solution was not accepted.

1. R
rbtroj

OMFG, I really am that stupid. Never mind. I just saw it … you have to include the blue squares on the same side of the line where you are subtracting them from the yellow ones.

3. R
Riley

The rule is: If you can completely subtract a set of yellow dots with an equal set of blue dots, it does not matter the size or shape of the area!