7 techniques for when you get stuck on Illustration Logic (advanced)
When the overlap method and working from the edges stop getting you anywhere, try the 7 techniques here. Each is explained on a board part-way through one of Puzzle Lounge's free puzzles. You can solve any puzzle in the diagrams on screen or print it. If you are new to this, or solving with a child, start with How to solve and tips and 5×5, and once you are used to it, try techniques 1-3.
First, check these when you get stuck
- Finished rows and columns: check that you have not forgotten to mark the rest of any row or column that already matches its numbers.
- Miscounts: count the filled squares again, using the thick lines every 5 squares as a guide.
- Lines where the numbers will not fit: if a row or column cannot take its numbers however you place them, there is a mistake somewhere. Go back to the last point you were sure of.
- Lines that changed: look again at the rows and columns through the last square you filled or marked. The next move is often close to what just changed.
If you are still stuck, look at the board and find its pattern in the table below. In this article, a square you have decided not to fill is called a "mark" (on paper, a square where you write a × or a dot). In the diagrams the navy × is a filled square (the game's embroidery look), and the small dot is a mark. Whatever is said about a row goes for a column too. On the boards, the line to look at has a red frame; in the diagram to its right, only the squares that technique settles have a red frame.
| If you see this | Try this technique |
|---|---|
| A filled square right next to a mark | 1. Next to a mark is like the edge of a row |
| A filled square in a row with one number | 2. Mark the squares out of reach |
| A run of filled squares as long as the biggest number | 3. Mark both sides of the longest run |
| Filled squares with one square between them | 4. Too long if joined? Mark the square between |
| A short gap shut in by marks or the edge of the row | 5. Never fill a gap that is too short |
| Marks split the row, and the biggest number fits in only one gap | 6. The overlap method inside a gap |
| Scattered filled squares, and you cannot tell which number they belong to | 7. Pack left and right to see which run is which |
We solved 137 of Puzzle Lounge's free puzzles and counted: "squares out of reach" had a use in 126 puzzles and "the longest run" in 134. "Too long if joined" (46) and "gaps too short" (58) come up less often, but they are worth knowing.
1Next to a mark is like the edge of a row
If a filled square sits right next to a mark, that is the end of its run. Once you know which number the run belongs to, you can fill its length, just as you would from the edge of the row. If the runs split off by marks match the numbers in count, they settle in order from the edge: number 1, then number 2. A mark in the middle of a row is easy to miss, so every time you make one, look next to it.
In 10×10 No.21, column 3 from the left is "3 3". The mark at square 5 splits the column into top and bottom. Squares 3 and 4 above the mark and square 6 below it are separate runs, so the top is number 1, "3", and the bottom is number 2, "3". The top run ends just above the mark, so extend it upward to squares 2-4, and mark square 1. The bottom run starts just below the mark, so extend it downward to squares 6-8, and mark the remaining squares 9 and 10 too.
2Mark the squares out of reach
In a row with one number, any filled square fixes how far that run can reach. A square it cannot reach however you place it stays empty.
In 10×10 No.1, column 2 from the left is "4". From the crossing rows, squares 6 and 7 are filled. The run of 4 must contain these 2 squares, so pushed to the top it covers squares 4-7, and pushed to the bottom squares 6-9. It cannot reach squares 1-3 or square 10, so mark them.
3Mark both sides of the longest run
When a run of filled squares reaches the length of that row's biggest number, it cannot grow. The squares just outside it on both sides stay empty. This works even when the other numbers are not settled yet.
In 10×10 No.11, column 5 from the left is "4 1 2". Squares 2-5 are a filled run of 4. The column's biggest number is 4, so this run cannot grow. Mark square 1 above and square 6 below. Where "1" and "2" go is not settled yet, but the extra marks give you the next clues.
4Too long if joined? Mark the square between
When filled squares sit with one square between them, and joining them would make a run longer than the biggest number, the square between stays empty.
In 10×10 No.1, column 5 from the left is "2 3". Squares 5 and 6 and squares 8 and 9 are filled, and square 7 between them is not settled yet. Fill square 7 and squares 5-9 join up into a run of 5. The column's biggest number is 3, so a run of 5 is impossible. Mark square 7. Now you know squares 5 and 6 are part of "2" and squares 8 and 9 part of "3".
5Never fill a gap that is too short
If a gap between marks is shorter than every number, nothing goes in it. The edge of a row works as a divider just like a mark.
In 15×15 No.5, row 13 from the top is "4 3". Squares 1 and 2 at the left end are a gap of 2 squares between the edge of the row and the mark at square 3. Squares 14 and 15 at the right end are also 2 squares, between the mark at square 13 and the edge. The numbers are 4 and 3, and neither fits in 2 squares. Mark these 4 squares.
6The overlap method inside a gap
When marks split a row, look for the gaps the biggest number fits in. If there is only one, the number is there. Treat the gap as a short row and use the overlap method.
In 10×10 No.9, column 7 from the left is "5 3". The mark at square 7 splits the column into 6 squares above and 3 below. "5" will not fit in 3 squares, so it is somewhere in the top 6. Push 5 squares up or down inside those 6, and squares 2-5 overlap either way. So you can fill squares 2-5.
7Pack left and right to see which run is which
When you have several filled squares but cannot tell which number each belongs to, try packing all the numbers to the left and then to the right (top and bottom for a column), respecting the filled squares and marks. Squares where the same number overlaps can be filled, and squares no number reaches are marks. It is the overlap method applied to a line part-way done.
In 10×10 No.7, column 3 from the left is "2 3". Squares 3, 5 and 7 are filled, and square 8 is marked. First pack the numbers upward. Put "2" on squares 1 and 2 and it touches the filled square 3 and becomes a run of 3, so "2" must be squares 2 and 3. "3" then goes, after a gap of 1, on squares 5-7. Next pack them downward. Below the mark at square 8 there are only 2 squares, and "3" will not fit, so "3" stays on squares 5-7. Move "2" to squares 3 and 4 and it touches "3", so it stays on squares 2 and 3. Packed up or down, the shape is the same, so it is settled. Mark squares 1, 4, 9 and 10.
A trial fill is the last resort
On hard paper puzzles you sometimes fill a square as a test and see whether it breaks the numbers. If you do, use a different colour pen or copy the board so far, so you can go back after a mistake. Every Puzzle Lounge puzzle can be solved without it.
Solve the puzzles in this article
All the puzzles in the diagrams are free. See the techniques turn up for yourself.
- 10×10 No.1Uses techniques 2 and 4Solve on screenPrint
- 10×10 No.7Uses technique 7Solve on screenPrint
- 10×10 No.9Uses technique 6Solve on screenPrint
- 10×10 No.11Uses technique 3Solve on screenPrint
- 10×10 No.21Uses technique 1Solve on screenPrint
- 15×15 No.5Uses technique 5Solve on screenPrint
How to read the numbers and what to start on are in How to solve Illustration Logic and tips. To follow one puzzle from start to finish, see Solving one 15×15 puzzle.
Questions
What do I do when I get stuck part-way through an Illustration Logic puzzle?
Work through "First, check these when you get stuck" in this article, in order. If you have not missed a mark or miscounted, pick the technique from the table that fits what you see on the board.
Do I need to fill a square as a test (proof by contradiction)?
Not on Puzzle Lounge's puzzles. Every one has been checked to lead to one picture working one line at a time. You may use it on hard puzzles on paper, but going back after a mistake is a lot of work, so keep it as a last resort.
Why do I get stuck so often on 15×15 and 20×20?
The bigger the puzzle, the more rows have lots of numbers, the bigger the slack tends to be (the squares left over once the numbers and the gaps between them are packed together), and the fewer squares the overlap method alone can fill. Mark often, look at the squares next to marks and at short gaps, and use the overlap method inside gaps, and you will get moving again.