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The Art of Puzzles - Mystery Kakuro

16 July 2006 @ 02:43 pm

Mystery Kakuro

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**motris**on July 17th, 2006 05:13 pm (UTC)

Not sure I understand the distinction you are making in the first part of your comment. I don't think I've ever seen a kakuro where the "same entry did not appear twice" as a rule, although this may be true de facto in smaller-sized puzzles. I interpret what you mean to be the order and identity of say 4 digits in a sum of 20 like "1982" from left to right occur twice. With the larger Nikoli puzzles I solve, there are so many occurrences of two digit clues like 16's or three digit 23's or similar clues that it is impossible to not say have 689 entered fewer than 2 or 3 times.

The other half of your comment is true though. Standard kakuro rules would say that within a single entry, no digit is repeated. 7 in 3 digits must be 1,2,4 and not 1,1,5 or 2,2,3 or 3,3,1. However, there are variations where this rule is not necessarily true, but I've only seen examples where the authors specifically told you that digits repeated with each entry having exactly one digit repeated twice. IIRC, four such examples are in one of the Tuller/Rios Mensa Puzzle Books, probably the orange one.

The other half of your comment is true though. Standard kakuro rules would say that within a single entry, no digit is repeated. 7 in 3 digits must be 1,2,4 and not 1,1,5 or 2,2,3 or 3,3,1. However, there are variations where this rule is not necessarily true, but I've only seen examples where the authors specifically told you that digits repeated with each entry having exactly one digit repeated twice. IIRC, four such examples are in one of the Tuller/Rios Mensa Puzzle Books, probably the orange one.

(Anonymous) on July 18th, 2006 07:44 am (UTC)

In the UK, 'Tough Puzzles' magazines always features several Kakuros (called 'Cross Sums') with the additional rule (stated) that "the exact same answer is never used more than once in the grid", i.e. order and identity of digits doesn't appear twice. I don't know if this carries over to the same publisher's spin-off mag (now renamed 'Kakuro'). Sorry for my lack of experience; and it didn't hamper solving this excellent puzzle.

(Anonymous) on July 18th, 2006 03:14 pm (UTC)

Don't apologize. It's in part my lack of experience with Tough Puzzles, having never done an issue as it seems somewhat expensive, considering importation fees as well as the normal cover price.

Its a unique kind of constraint, and if well constructed could make for an interesting additional part of a cross-sums puzzle. I could actually imagine a similar kind of "sudoku" constraint that you could build into a puzzle; in its simplest form it would be, the same 3 digits to complete a row/column in a nonet cannot be used in the same order to complete another row/column in another nonet. An even harder form would be, the same 3 digits in any order that complete a row/column in a nonet cannot be used to complete another row/column in that nonet. It would get around my "least favorite" sudoku grid fills where the three digits in R123C1 are also in R456C2 and R789C3 in some order (or variants thereof).

Its a unique kind of constraint, and if well constructed could make for an interesting additional part of a cross-sums puzzle. I could actually imagine a similar kind of "sudoku" constraint that you could build into a puzzle; in its simplest form it would be, the same 3 digits to complete a row/column in a nonet cannot be used in the same order to complete another row/column in another nonet. An even harder form would be, the same 3 digits in any order that complete a row/column in a nonet cannot be used to complete another row/column in that nonet. It would get around my "least favorite" sudoku grid fills where the three digits in R123C1 are also in R456C2 and R789C3 in some order (or variants thereof).