How to solve Slant puzzles without guessing

Start with the zeros

A zero means no diagonal may end at that dot. Each square next to it has two possible diagonals, but only one avoids the zero. Draw that one.

An edge zero fixes two squares, and a corner zero fixes one. Count only squares that actually exist inside the board. An interior zero would force a closed diamond of lines around it, so it cannot appear in a valid Slant puzzle.

Look for clues that need every available line

An interior dot has four neighbouring squares. If its clue is 4, every one of those squares must point towards it. The equivalent clue on a straight edge is 2; at a corner it is 1.

This rule still works halfway through a puzzle. Suppose a 3 already has two touching lines and only one undecided square could supply another. That last square must touch the dot.

Turn away from a satisfied clue

Once a dot has exactly the number of touching lines it needs, any remaining neighbouring squares must point away. For example, a 1 with one touching line cannot accept another.

Keep checking both endpoints of each new diagonal. A move forced by one clue may finish a second clue, which can force another move further along the board.

Use the no-loop rule

Slant forbids every closed loop, even if all the numbers around it would be satisfied. When one choice joins the ends of an existing path into a loop, choose the other diagonal.

The illustration shows three sides of a diamond already drawn. The dashed fourth side would close the loop, so the last square must take its other diagonal. Branches are allowed, and separate networks do not have to join.

When the easy moves run out

Make another pass through the board: zeros, clues needing every remaining connection, satisfied clues, then possible loops. A line you added elsewhere may have changed what is forced.

Larger boards can need deductions involving several clues together. If you use a hint, read the explanation and work out what changed before taking another. A hint in HubbardGames adds time; the ordinary clue colours check public rules, not the hidden answer.

• Count lines touching the dot, not lines merely near it.
• Never leave a square blank at the finish, even if its corners have no numbers.
• A green clue is locally satisfied; it does not prove the entire board is correct.