Taxicab-kuro II
(Published on 25. July 2020, 08:00 by glum_hippo)
Because of the uniform layout of the first Taxicabkuro some of the typical logical tricks of Kakuro were not available. Here is an attempt to incorporate some of these in certain places. Have fun!
Standard Kakuro rules apply. Each cell must contain a digit from 1-9, such that no digit repeats within a 'word' and the digits add up to the clued value.
Also there is a 'Manhattan distance' or 'anti-taxicab' restriction: if two cells contain the same digit, the taxicab distance (minimum number of orthogonal steps from point A to point B) cannot be equal to that digit.
Example: in the following diagram, due to the givens, 7 is excluded from all blue and green cells, and 4 is excluded from all red and green cells. As one can see, the blackened cells are treated like any other cell in the way the Manhattan distance is calculated. Please note that e.g., the 7 also excludes a 7 that is seven steps directly above it in the column or seven steps directly to the right in the same row! (From Taxicab-Sudoku one is perhaps accustomed to looking for shifts in two perpendicular directions)
And here is the puzzle. The grey cells are just to help with counting and have no influence on the logic. Try it on Penpa!
Solution code: The bottom row (unclued sum, then 30-sum and 20-sum); then the 5th column of numbers (the 9-sum and the 31-sum). 21 digits total
Comments
on 9. February 2022, 13:34 by glum_hippo
updated link
on 19. October 2021, 07:40 by Mark Sweep
I definitely liked this one better than puzzle I. Indeed Kakuro logic seemed a bit more pronounced and I felt like the taxicab logic may have been better telegraphed or at least the solve felt more linear in a way, making it less likely to get lost in the grid. Enjoyed it very much!
—— I'm glad to hear it; I can now disclose that I've done about 3 more attempts to create a truly 'approachable' taxicab-kuro, but they all contained loopholes into hard elimination rounds. Still working on that!
