# Snakes and Adders - A New Grid Puzzle

So, literally last night, I dreamt of this new grid puzzle genre, so I'm just giving it a shot...

1. Put some snakes into the grid on the white cells.
2. Each snake forms a sequential chain of cells connected horizontally and vertically from its head with '1' to its tail with 'N' where N is the length of the snake.
3. The length of each snake must be inside the given range on the top-right corner.
4. Snakes cannot touch other snakes horizontally or vertically, but diagonally is allowed. However, snakes can touch themselves.
5. The clue denotes the sum of the snake numbers adjacent to it including diagonals.

• I think rule 5 should read "sum of the adjacent snake numbers". Right? Feb 23, 2022 at 21:39
• Very late to the party, but a Penpa link for interested solvers. Apr 18, 2022 at 17:12
• This puzzle is a nomination for Best Puzzles of 2022: January - March! May 19, 2022 at 23:28

The complete grid

If we first look at this cell

since it's a high number and only 4 surrounding cells.

we see that we get three potential snake-formations, with sum 14, surrounding that cell.

OR

OR

Now, if we focus on this cell

it becomes clear that the only formation (in the previous case) that works is the second one.