How to Solve Snake Puzzles
Snake is one of those puzzles with unclear origins. Your goal is to shade cells to form the body of the snake within the grid. The head and tail are given. Another common theme is that of a tunnel, with the entrance and exit given.
Rules
Given the head and tail of a snake, use number clues to shade cells containing the snake’s body.
- The path forming the snake’s body is exactly one cell wide.
- This path follows a contiguous group of cells that moves only in orthogonal directions.
- No part of the body touches itself, not even diagonally.
- Numbers on the edges of the grid indicate how many cells within that row or column are part of the body.
- Rows or columns without a clue number have an unknown number of filled-in cells, not necessarily zero.
The body path may not move diagonally. 
The path of the snake’s body may not touch itself. 
No, not even diagonally.
Basic Techniques to Solve
- Start by eliminating cells in rows or columns with a 0 or 1 clue.
- Think of the grid in terms of “zones.”
- Look at stripes along the edge.
- Use a common nonogram technique for large clues.
- Mark cells that must be eliminated as you solve.
- Use corners to narrow your options down.
Eliminate Cells with Small Clues
Typically in shading puzzles, an important task is to mark cells that you know to be unshaded. This provides restrictions to make finding shaded cells easier. Marking a row or column with a clue of zero is obvious. For those with a clue of one, look at the rows or columns that cross it. To cross a row or column which contains only one body segment requires a stripe of 3 cells, unless that single cell is the head or tail itself. This means you can immediately mark crossings where that row or column clue is 1 or 2 as unshaded.
Grid Zones
Clues of 1 or 2 in the middle of the grid effectively divide the playfield into separate areas, because crossing them either prevents crossing back, or crossing a maximum of twice. Thinking about the grid in these terms helps with other clues. Simply, you must complete some clues entirely on one side of the crossing. This will come into play when we examine nonogram techniques later.
As you just saw, a 1 clue forces a single crossing. A 2 clue results in two possibilities. Perhaps it’s a single crossing in which the snake enters, moves one cell along that row/column, then exits. The other option is that the two shaded cells are separated, forming a bend in the path, like a U-shape.
By visualizing the “zones” of the grid, you can see it as sub-grids. Thinking through this sometimes gives you an idea of the path the snake’s body has to take.
Edge Stripes
An interesting thing to remember is that a stripe of cells on the edge of the grid can never be fewer than 2 cells long, unless it contains the head or tail. This is because of the rule about the body not touching itself. The snake body can’t travel to the edge, then immediately do a U-turn within 2 cells, because that immediately creates a 2×2 area, violating the 1-cell-wide rule.
So if the snake touches the edge and turns around, it must first follow the border for at least 3 cells, unless the head or tail is on that edge. As a result, any time you have a clue between 3 and 5 along an edge anywhere in the middle of the snake body, it must be a single stripe of cells, rather than split. This way of thinking pairs very well with the visualization of zones that we just discussed.
Consider this 4 row. The 2 right below it must be a dual crossing because of all the other clues. That means a U with a stripe of 4 contiguous cells. But where? 
Neither leg of the U can cross these cells, because it would have to be a stripe of 3, violating the 2 clues. We saw that issue when we looked at the 1 rows. 
Once we eliminate those cells, we’ve revealed the only possible path for our U-shape.
Think Nonograms
If you’re familiar with nonogram puzzles, you know that a common technique with large clues is to start at each of the extreme ends of that row or column and count cells. If you find an overlap in the middle, you know you can shade those cells no matter which end you’d start from.
In a Snake puzzle, you can also use this method, and here is another place where “zone” thinking comes into play. Imagine those crossings as dividing lines. If the clue you’re looking at must be complete before the crossing, the extreme ends of that row or column must be closer together, which means a greater chance of overlapping cells.
Another way you can look at it, especially in rows and columns with large clues, is how many cells must be empty. Sometimes you can use required gaps to figure out how the snake moves through an area.
Dead Cells
As you solve the puzzle, watch for dead cells. This relates to the rule about the snake touching itself.
Whenever you create a known stripe of 3 or more cells, mark cells adjacent to the middle of that stripe as eliminated, because they can no longer contain part of the snake’s body.
Similarly, if you’ve created a known corner, you can eliminate some cells around it.
Finally, mark out any dead ends that develop as you eliminate other cells.
In this case, none of these three cells can be part of the path. If they were, they’d be part of a segment touching the middle of these known pieces of the body.
Corner Elimination
Look for corners you create by eliminating cells around it. Corners are any cell with only one entry and exit point that are 90-degrees apart, not just at the edge of the grid. If the snake enters this corner, it’must move in one of two ways:
- The path uses at least 3 cells on each leg, creating a long L-shape, or
- The path zig-zags, forming a W-shape. You’ll sometimes see this when crossing a zone boundary.
Combine this knowledge with the clues around corners you create during the solve. Doing so often helps you to eliminate cells from the possible path, usually by forcing a situation where you will exceed or fall short of a clue’s requirement.
Entering the corner, the snake can’t simply bend back on itself. That breaks the “no touching” rule. 
So in a hard corner, it usually requires at least 3 cells on each end to turn, unless the head or tail is involved. I placed the eliminated cell this creates. 
Occasionally, the snake zig-zags instead. You’ll often see this crossing a zone boundary. Here, the eliminated cells, force each end to extend one more cell..
Solving the Puzzle
That should give us a solid foundation of tips to work out most Snake puzzles. Now it’s time to move on to the walkthrough solve of our main example. However, if you’d like to try solving the puzzles used in this tutorial, you can attempt them below:
Entering the Zone
We’ll start with the top row, because it requires 9 our of 10 cells to be shaded. Here we see the gap can’t be at either end, because that would eliminate too many cells to fulfill the 5 clue below it. 
Then, using the corners technique, we’ve solved these cells, and marked those eliminated in the process. 
Next, we’ll look at this zone boundary. If we use either of the cells next to the head, we’d cut off part of the snake whether we go up or down afterward. So there must be a second crossing.
Now what if the head moves up? It would either connect to the tail early, or it would connect on the right. But only one of the two segments can cross the boundary, so the other would get cut off. 
We can also deduce that the second crossing must be in one of these three cells. If the tail crossed down without connecting to the right segment, they wouldn’t be able to connect later. 
Now let’s consider this zone crossing. If the tail simply moves straight through, it forces the second crossing to be in the bottom area of the grid. But then it’s one-way, so it’s invalid. The tail moves down and to the right.
That tells us where the gap is in the 9 row, so we can easily solve it and the remaining cells in the 5 row. Notice we used both cells in this zone crossing. 
When we mark the unused cells in the rows and columns we just completed, we cut off a lot of cells. So let’s eliminate them. 
Now there are only five cells remaining in the bottom row. This completes the clue, so all of them are used.
Connecting the Snake
Using our corner rule, we must extend up two cells at each end. That completes the 2 row, so they must go up one more cell. 
We also completed this 2 column, so we can eliminate all its remaining cells. 
Once we do that, there are exactly enough cells left to complete the 4 row. So again, all of them must be used.
This corner forces us to move down and connect to the next body segment. It also completes the 3 row, so the snake moves up and connects again. 
Finally, we discover the correct second crossing of this zone boundary. Once we shade it in, we’ll reach the tail. 
We’ve completed the Snake puzzle!
