No-Left-Turn Mazes

The finish can sit one passage away and still be illegal to enter. No-left-turn mazes require you to track the direction you're facing as well as the place where you're standing.

A left turn means a turn to your own left relative to that heading. West may be legal; east may be forbidden. It depends on how you arrived.

Ordinary corridor mazes usually allow either turn at an open junction. This extra restriction belongs to a family of directional logic puzzles, introduced alongside other formats in the brain-teaser guide.

State the rules precisely

For the worked example and Practice A, you may go straight, turn right, or make a U-turn. Left turns are forbidden. Practice B allows straight and right moves but forbids U-turns.

Every move follows a drawn connection to the next marked node. You cannot rotate in place, leave the network, or combine several stationary rotations to manufacture a legal-looking heading. A U-turn, when allowed, reverses your travel along an existing connection.

Creators vary their restrictions. Do You Maze's directional-maze guide describes several direction-based rule sets. Read the individual puzzle's U-turn rule before applying a strategy from another sheet.

Track position plus heading

Write a state as (cell, heading). For example, (J, S) means you are at junction J and facing south.

The states (J, S) and (J, N) offer different legal exits. When you face south, east is a left turn. When you face north, east is a right turn.

Be careful with everyday wording. Entering from the north means traveling south. Entering from the south means traveling north. Saying "face the direction you came from" would point you backward; keep facing the direction you were traveling as you entered.

A small arrow beside your pencil mark is enough to record that distinction. Place it along the incoming passage, pointing into the junction.

Revisiting a cell with a different heading can be necessary. Marking the entire cell as permanently used would throw away a potentially useful state.

For these fixed-rule puzzles, arriving at exactly the same cell with exactly the same heading recreates the same options. During systematic search, you can stop expanding that repeated state. A variant with switches or collected keys would require recording those changes too.

A solving method

1. Mark the starting arrow before moving.
2. At each node, keep facing the direction of your last move.
3. Cross out the immediate left option on your working copy.
4. Consider straight and right. Add reverse only if the sheet permits U-turns.
5. Move along one connection and record the new heading.
6. When an attempt fails, return to an earlier decision in your notes and try another legal sequence.

That last step is search backtracking. Erasing an attempted route doesn't mean the token physically walks backward. If you're moving a token in play, every return movement must obey the puzzle's rules.

Use a tracker when several visits overlap.

Print the heading tracker for longer attempts. Writing just the node and compass letter usually leaves enough room to follow your reasoning later.

Worked example with an allowed U-turn

Start at S facing east. The diagram's named nodes are connected only where a passage is drawn. U-turns are allowed on this sheet.

The connections are S-A, A-B, B-J, J-D, and J-F. S, A, and B share the top row. J sits below B, D sits below J, and F is immediately east of J.

1. Move from S to A, continuing east.
2. Continue east from A to B.
3. Turn right at B and move south to J.
4. At J, the finish branch points east. You're facing south, so that branch would require a forbidden left turn. Continue straight south to D.
5. D is a dead end. Make the allowed U-turn and move north to J.
6. You now face north at J. Turn right into F, traveling east.

The route is S, A, B, J, D, J, F. Visiting J twice is essential in this network. The second arrival changes which turn reaches the goal legally.

If this same sheet forbade U-turns, D would trap the attempt. There is no alternative loop here to supply a north-facing return to J, so the worked network would have no solution under that changed rule.

Practice A - U-turns allowed

Start at P facing south. Reach F. Straight moves, right turns, and U-turns are allowed; left turns and stationary rotations are forbidden.

The first turn carries you west toward J. Before choosing its finish branch, write your heading beside the junction.

Practice B - U-turns forbidden

Start at S facing south and finish at F. Follow only drawn connections. You may go straight or turn right, and you may revisit nodes. U-turns, left turns, and stationary rotations are forbidden.

Try this one without reversing at a dead end. The outside connections let you return to the central junction with a different heading.

The keys give one verified route for each practice network. Repeating a legal loop can produce longer walks, so "one answer" shouldn't be interpreted as banning every valid detour.

Check a proposed answer one move at a time

A list of connected nodes can still contain an illegal turn. Check the worked answer by writing its headings: east, east, south, south, north, east. Compared with the starting eastward heading, the actions are straight, straight, right, straight, U-turn, right. Every transition fits the worked sheet's rules.

Now inspect the tempting shortcut S, A, B, J, F. All four connections exist. The failure occurs only at J, where southward travel changes to eastward travel. That is a left turn. A useful correction identifies that exact transition rather than dismissing the whole route as wrong.

When checking a partner's solution, cover the later moves and replay from the printed starting arrow. At each node, ask whether the next connection exists, then whether the change in heading is permitted. Reaching F doesn't excuse an earlier illegal move.

If your headings disagree with the answer card, return to the first disagreement. Later turns depend on the direction established there, so correcting only the final arrow can leave the underlying mistake untouched.

Why reversing a solution can fail

Ordinary undirected corridors can be walked in either direction. A no-left-turn rule changes that relationship because a forward right turn becomes a left turn when the same route is traversed backward.

In the worked example, you reach B traveling east, then turn right toward J to travel south. Reverse those movements: traveling from J to B brings you north, and leaving B toward A requires a westward move. North to west is a forbidden left turn.

You can still reason backward from F, but check each proposed predecessor using the heading a forward-moving token would have. Don't take an ordinary exit-to-start trace and assume reversing its node list will produce a legal solution.

For a hint without revealing the route, begin with the last junction: which arrival heading makes the finish branch legal? Then ask where that heading could come from. This keeps the search focused on a specific missing approach instead of encouraging repeated guesses at the branch nearest the goal.

Common mistakes

Treating left as west ignores heading. Use the compass table until relative directions feel comfortable.

Forgetting the new heading after a turn makes the next junction unreliable. Record the arrow immediately after moving.

Revisits aren't automatically errors. Compare both the location and the direction of arrival before discarding a state.

Don't borrow a U-turn permission from a neighboring worksheet. It belongs on each puzzle's own rule label.

Standard wall-following can demand a left turn or a reversal. Check every move against the additional constraint rather than assuming an ordinary maze technique remains legal.

Related reading

Maze-solving algorithms explain ordinary corridor strategies. Hard printable mazes offer a separate navigation challenge without this page's added no-left-turn condition. Unless a worksheet says otherwise, you can use either direction at its open junctions.