Kakuro Variant
So one of the comments I remembered reading post-qualifying test was that someone wished there was a magazine filled with just kakuro variations. I must admit that, unlike sudoku which can vary in many many ways to create a range of neat new puzzles, I think kakuro seems to not have as many routes available to it. That won't stop me from trying to offer some unique puzzles here over the coming months.



A lot of challenging variations already exist (I may not be using common names for these, but then I don't know that common names exist). Examples include "Zero Kakuro" where the use of 0 is permitted, "repeated digit kakuro" as in the Tuller/Rios books where each entry has a digit repeated twice in it (23 can be 9+9+5 or 8+8+7 or 7+7+9 but not 9+8+6), and "missing/incorrect sum kakuro" where there are either missing clues, or the clues are wrong by, say, one unit in either direction. Last week saw a good example of "plus/minus kakuro". There might be the possibility for a variation like "mod-10 kakuro" where the clues only reveal the ones-digit of the entry. I may try this idea sometime in the future.

One variant which occurred in a more complicated sudoku/kakuro form in the 2004 USPC was a "consecutive digit" puzzle where each and every instance of two digits vertically or horizontally adjacent that were consecutive would be marked.

This variant, particularly in the sudoku realm, is one of my favorites when it is "clean". Imagine a "Consecutive Kakuro" or "Consecutive Sudoku" where none of the digits ever touches a neighbor that is just one away. While it would still fit into the "Consecutive" category, it would be more accurately described as a "Non-consecutive" puzzle. The puzzle below is a Non-Consecutive Kakuro of exactly this type. For each row/column, the preceding number indicates the sum of that row/column. Only the digits 1 through 9 are used for each sum, and at most once in each sum. Further, no two adjacent digits can be consecutive numbers.

You will see that this adds some interesting constraints to kakuro (6 can no longer be a 3 digit clue as 1-2-3 has no entry that is valid; 30 must be 8-6-9-7 or 7-9-6-8; and a whole host of others for you to discover on your own). I tried to make the following puzzle have some easily solvable parts, some much harder parts, and some areas that are likely not possible until you solve others around them. In other words, I think it a fun, fair, and difficult challenge. It can be solved completely by logic alone and has a unique solution. Enjoy.