On a large board, finding every block with two neighbours will not always fix the whole route. Try asking, "What happens if I do not use this link?" We will find one complete route through all 42 blocks of Level 42. This board has multiple solutions, so not every choice below is forced.
Reasoning links and the playable line
Start at the white ring, move orthogonally through every block once, and finish on the star. Ordinary blocks need two links; the ring and star need one each. Separate pieces of line in the diagrams mark inferred connections. In the game, draw one continuous line from the ring. Count rows from the top and columns from the left.
Level 42. The ring is at row seven, column two; the star is at row three, column one.
Hint 1: Collect the certain links first
Link the blocks with only two neighbours and the ring's only exit. Then propagate the links forced by blocks that already have two connections.
Hint 2: Remove a link in your head and look for a loop
The link from row three, column two to the cell below is required. Without it, the left-hand links close into a loop.
Assume that link is absent. The cell in row three, column two must then use both left and right links. The cell below must use left and down. Combined with the existing links, they close a loop. Such a loop cannot connect the ring to the rest of the board. The assumption fails, so the removed vertical link is required.
Hint 3: Separate forced links from choices
Choose the downward link from row one, column five, then downward again from row two, column five. Cross out links that would close small loops.
Neither of these branches has only one valid answer. We are choosing one route that can reach the finish. After a choice, close other links at blocks that already have two, and reject links joining the two ends of one piece into a loop. A link forced by contradiction is different from one selected among valid alternatives.
Apply the same test below row three, column four. Removing its downward link forces horizontal links that close a loop. Keep the vertical link, then choose the next branch.
Hint 4: Do not finish at the star too early
Cross out the link between columns four and five of row six. It would join the ring-side and star-side pieces while blocks are still left outside.
A route can finish too early without forming a loop. Once the ring is connected to the star, neither end can be extended to take in leftover blocks. Join those pieces only after every block is included.
Removing the link between columns five and six of row five would connect ring and star too soon. Keep it, choose the remaining branch, and complete the last two links.One completed route: start at the ring, visit all 42 blocks once, and finish on the star.
TipKeep the trial short. Remove one link and follow only a few nearby forced links to see whether a loop or early finish appears. Failing to find an immediate contradiction does not prove the link is wrong.
Block Link The JoyPlus Soft Planning Team
