Let's try putting in random numbers that seem to make sense. Let's put a 2 to finish that 2 off down in the bottom right:
(whenever solving a puzzle in these tips, new info will be in red, while all previously added info will be green)
Now, I like that 4 at the top having these other 4s as well...
Wait a minute... That two in the upper-right isn't complete! All is lost!
...that's why this is NOT how you do logic puzzles. For a puzzle to be a logic puzzle, there must be EXACTLY ONE solution. No more, no less. (If you think one of my puzzles has no solution or more than one solution, please email me (sudgylacmoe@gmail.com) with why you think so so that I can fix it as soon as possible.) You put in information that MUST be true, not what MAY be true. You need to use logic to solve them (hence the name "logic puzzle"). Here's how you would solve it:
First, we can close off the 1 because it can't do anything else. That actually could have happened last time, but I didn't feel like it.
Now look at that three on the top row (rows are horizontal, while columns are vertical). It can go left, but only once. There needs to be three threes in that polyomino. It can't get them just by going left, so it MUST go down at least one:
The four in the top row is the same; it can only go right one, so MUST go down two. This connects it with the other four in the third row and fourth column (row 3 column 4, or just R3C4) and closes it off:
Now, look at that two in R2C4 (second row, fourth column). It can only go one way, up:
The rules say that polyominoes of the same number can not touch each other. Thus, all of these threes can't touch or it would be way too big:
Now, all of these threes and twos have only one way to go, so their solving is really easy:
What about that extra spot? Well, the polyominoes don't need to have any number originally in the puzzle, so the puzzle is solved if we put a 1 in there:
And the puzzle is now solved. So, to solve a logic puzzle, you see what MUST be there, and using this information, keep on figuring out what MUST be somewhere else, and you eventually have solved the puzzle.
Solving puzzles is usually based on two things: what I'll call "theorems", and just pure logical thinking. In a logic puzzle, a theorem is basically a technique that can be used when you see a certain pattern. An example that we used in the above puzzle (that's really obvious) is "If a polyomino can only go one direction, that number must be put in that cell." We used it a lot in that second-to-last image. Theorems are unique to each type of logic puzzle, and is what the specific puzzle tip pages are mostly about.
Pure logical thinking is hard to teach, so for most puzzles there is an example puzzle that is solved at the bottom of the page.
Another useful thing when solving logic puzzles is to mark any information, even if it's not specifically a part of the solution. I'll go into this more for each type of puzzle. I used this in the third-to-last image above, where I just drew lines to help me solve the puzzle.
One theorem that stands in any logic puzzle is this: If an (open) area has multiple solutions, anything shared by all solutions is true. I'll color things blue when I'm doing this.
One last thing: there's a technique that I personally hate called "bifurcation". It's where you assume something, see where it leads, and if it at some point reaches a contradiction, your original assumption is wrong. I try not to use it in my puzzles (but did once by accident), but it's a good technique to know. I'm alright with a very small amount of bifurcation (the smallest amounts are actually what you use to solve logic puzzles normally). Any time I bifurcate, I'll also color it blue (because I'm thinking of a possibility).
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