Str8ts

Str8ts is a logic-based number-placement puzzle distinct from but sharing some properties and rules with Sudoku. The solver is asked to fill the remaining white cells with numbers 1 to 9 (or 1 to n in puzzles with N cells per side) such that each row and column contains unique digits. Whereas Sudoku has the additional constraint of 3x3 boxes in Str8ts rows and columns are divided by black cells into compartments. Each compartment - vertically or horizontally much contain a straight - A Straight is a set of numbers with no gaps and in any order. For example,
[7][6][4][5] is valid but [1][3][8][7] is not.
Additional clues are set in the black cells - these numbers remove that digit as an option in the row and column. Such digits do not form part of any straight.

History

A hand made prototype of Str8ts which used black cells and the new rule of straights in compartments was invented by Canadian puzzle designer Jeff Widderich in 2007. He approached Andrew Stuart, a UK-based puzzle maker and programmer - to make the puzzle. Their collaboration settled how the clues would be determined and finalised the rules. The first daily puzzle was published on 24th of November 2007 at [www.str8ts.com].

Setting the clues

Black cell clues are chosen in the following way: Given a completed str8ts puzzle there will be some unused digits in each row and column. This maybe zero, or it maybe several digits in some black cells. Where there is no remaining digit the black cell remains empty. From the available remainder digits a set is chosen that does not repeat a number.

White cell clues are determined in a similar way to Sudoku. From a completed puzzle numbers are continually deducted until the puzzle no longer contains a unique solution. The last unique solution should contain the minimum number of clues - although numerous different puzzles could be made depending on the order of the selection of cells. The black cell clues are taken into consideration when solving the puzzle in each removal loop.

Grading

Str8ts puzzles can range from very easy to very hard in a manner similar to Sudoku. The grade is determined by a combination of opportunities to solve at each stage and the difficulty of the strategy that grants each solution. An easier puzzle will have many places where a logical deduction can place a solution or eliminate a candidate number. When the whole puzzle is assessed in this way, plus some heuristics, a score can be determined. Over a large number of puzzles (>10,000) a bell curve of scores can be produced. This can be quartiled to group puzzles into specific grades.

Properties of Str8ts

The distribution of black cells - either symmetrically or asymmetrically - leads to a massive number of possible templates (Sudoku has one). Combined with the very large number of digit placements in the white cells leads to a very large number of possible puzzles. The density of clues in a good puzzle is similar to Sudoku and like Sudoku the number of clues does not determine the grade. A very difficult Str8ts puzzle might have many clues while one that unfolds easily might start with relatively few clues.

Strategies

To be entered