Lockout Lines Sudoku: Rules and Solving Strategy

Understand the endpoint and outside-range rules

Lockout Lines Sudoku keeps the classic rule that every row, column, and 3x3 box contains the digits 1 through 9 exactly once. Each lockout segment has two endpoint cells, usually shown as diamonds, connected by a line. The endpoint digits must differ by at least 4. Every other digit on that line must be different from both endpoints and must lie outside the numerical interval between them. If the endpoints are 3 and 7, an interior line cell may use only 1, 2, 8, or 9. Digits 3 through 7 are locked out. If the endpoints are 1 and 5, the interior must be above the interval, so only 6, 7, 8, or 9 can appear. Digits may repeat along a line when ordinary Sudoku rules allow them. A diamond normally ends one segment, so when several segments meet you should treat each pair of endpoints independently. Shapedoku itself uses classic shape Sudoku without numerical line constraints, but the habit of maintaining accurate Notes transfers directly.

Use the endpoint gap before guessing exact values

Start with possible endpoint pairs rather than individual interior cells. Since the endpoints differ by at least 4, many candidate combinations disappear immediately. If one endpoint can only be 4, 5, or 6 and the other can only be 6, 7, or 8, test the pairs by their difference and keep only those separated by 4 or more. Then inspect the interior. A surviving endpoint pair is useful only if every line cell has at least one candidate outside its forbidden interval. This support test can eliminate endpoint pairs even when neither endpoint is solved. One especially useful fact is that 5 cannot appear as an interior digit on a standard Lockout Line. For 5 to lie outside the endpoint interval, both endpoints would need to be below 5 or both above 5. There are not two digits on either side that can still differ by at least 4. The digit 5 may be an endpoint, but never an interior line value under the standard rule.

Let interior digits push information back to the endpoints

Do not treat the endpoints as the only source of information. An interior placement also restricts the endpoint pair. If an interior cell is 8, the two endpoints cannot straddle 8 and cannot equal 8, so their interval must lie entirely below 8. Combined with the minimum gap of 4, that can sharply reduce the pair. Several interior digits are even stronger because every one of them must lie outside the same endpoint interval. Suppose one line contains confirmed interior digits 2 and 9. The endpoint interval must sit between those extremes without including either one, which pushes the endpoints inward while still keeping them at least 4 apart. Rows, columns, and boxes then decide which endpoint takes which value. Long line portions inside one unit can also create subsets because repeated digits are forbidden there by normal Sudoku rules. After every line elimination, rescan the affected units for singles, pairs, and locked candidates. The variant becomes much easier when you alternate range logic with ordinary Sudoku instead of trying to solve the entire line in isolation.

1. Identify each independent Lockout Line segment and its two endpoint cells.
2. Remove endpoint pairs whose digits differ by less than 4.
3. For each surviving pair, remove all interior digits inside or equal to the endpoint interval.
4. Remember that 5 cannot be an interior Lockout Line digit under the standard rule.
5. Use confirmed interior digits to restrict which endpoint intervals remain possible.
6. Return to rows, columns, and boxes after each range elimination creates new candidate pressure.