Logic Masters Deutschland e.V.

tl;dr The main puzzle link. (The solution code is the top row.) The 4x4 practice puzzle link.

I noticed I haven't seen any sudoku + icebarn hybrids, so I decided to make one! I was also inspired by mathpesto, who has made excellent hybrids of other pencil-puzzle genres with sudoku. This puzzle is designed around the interactions of several mechanics to construct your own icebarn puzzle (which then helps to solve the sudoku puzzle). For those who are unfamiliar, an icebarn puzzle consists of several 'icy regions' on a grid, and the goal of the puzzle is to draw a path from the 'in' arrow to the 'out' arrow which passes through every region at least once. The rules for a standard icebarn puzzle, together with examples, can be found at this link.

Rules of this puzzle:

• Standard sudoku rules apply.
• Nurikabe-lite. Every cell is either ice or ground. No 2x2 area consists only of ice cells or ground cells. Additionally, every ground cell must belong to an orthogonally connected region of at least 4 ground cells.
• Arrows. Each arrow in the grid is one of two types of clues, which you must determine. If an arrow is on an ice cell, it indicates the number of ice cells in the orthogonally connected ice-region containing the cell. (In this case, the direction of the arrow has no meaning.) If an arrow is on a ground cell, it acts as an 'icebarn arrow', explained below.
• Icebarn. Draw a single green path from the 'in' arrow to the 'out' arrow which passes over every icebarn arrow (in the direction indicated by the arrow), and only travels vertically and horizontally. The start and end of the path has been given. Additionally:
  • The path must travel straight through ice cells, and can only turn on ground cells.
  • The path cannot branch or loop, but two orthogonal segments of the path can intersect each other in an ice cell (and never on a ground cell).
  • Every orthogonally connected region of ice cells must be visited by the path at least once.
  • The digit on an icebarn arrow indicates the number of cells the path traverses from the arrow before it turns. (This means the number of cells from the arrow to the turn, including the cell with the arrow, but not including the cell where the path turns.)
• For clarity, on every cell containing an icebarn arrow, the path must both enter the cell and exit the cell in the direction of the arrow.

The rules may appear intimidating! The following is a 4x4 practice puzzle which attempts to minimise logic and maximise 'understanding the rules'.

Finally, the following is an example grid to demonstrate the icebarn rules. (The sudoku hasn't been completed, but the pencil-marks are the correct digits for this grid as determined via arrow rules.)