## Paint-by-sudoku (Japanese Sum + Hanjie variation)

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Paint-by-sudoku (Japanese Sum + Hanjie variation)

When I was visiting family for the holidays, my father was solving the "Paint By Sudoku" book that was out in the States, which is just a bunch of Paint By Number/Hanjie puzzles and has nothing to do with sudoku. I thought I should finally construct some puzzles that are truly paint-by-sudoku (I had made an earlier attempt, but this is much better).

This variation uses the standard style of a japanese sum puzzle in its outer constraints. The outside numbers refer to the sums of consecutive touching digits (or a single digit) as they appear in order in the puzzle by row/column with at least one space present between any region. If an outside constraint is, say, 15, then there must be a set of numbers (12345, or 69, or many other choices) that sum up to 15 in that row/column. If an outside constraint is 15 and then 9, then there must be a set of numbers that sum to 15, then at least one "space", and then a set of number(s) that sums to 9.

In this painting variation, you are actually meant to shade in the regions that are indicated by the outside numbers and at the end of the puzzle you will have both a valid sudoku and a fitting picture. People who like Killer Sudoku or Kakuro will appreciate how sums must be used in these puzzles to proceed.

I've written up a little more on my blog as well as made a new Hanjie variation here (with solutions), but the three paint-by-sudoku puzzles I'm sharing with indicated difficulties are below.

motris

Posts: 71
Joined: 13 March 2006

This looks very interesting. Could you give me more details and your website?
Comerscroft

Posts: 1
Joined: 16 December 2006

Hi,
I too found this very interesting variant which really uses technique from both worlds.
I could solve the easy one without problems and enjoyed it. Then I moved to the "pretty hard" one, but I get stuck to here.
I'm familiar with killer, but not really with Hanjie/gridler. So I may have missed some Hanjie technique here.
TIA for any hint.

+-----------------+--------------+------------------+
| 1 4789 46789 | 259 24 4579 | 4569 4569 3 |
| 3 5 2 | 6 1 49 | 49 8 7 |
| 679 479 4679 | 3 8 4579 | 14569 14569 2 |
+-----------------+--------------+------------------+
| 6789 2789 6789 | 1 57 3 | 24589 2459 5689 |
| 4 23 5 | 8 9 6 | 7 23 1 |
| 6789 1 36789 | 4 57 2 | 3589 59 5689 |
+-----------------+--------------+------------------+
| 579 3479 479 | 2579 6 4589 | 12 123 589 |
| 589 6 3489 | 259 24 1 | 23 7 59 |
| 2 79 1 | 579 3 589 | 5689 569 4 |
+-----------------+--------------+------------------+

Skipping singles & other "basic" sudoku techniques

45 on R3 -> R3C9 = 2
45 on C3 -> R9C3 = 1

In R6 : 3 <> {12} = 1 cell = 3
-> R6C8 <> 3 = {59}
5 <> {14|23} = 1 cell = 5
X-Wing on 3 in R68C37 -> not elsewhere in C37

C4:
19 = 3..5 cells
For 3 cells, only one possible combination : R567C4 = [847]
For 4 cells, only one possible combination : R1..4C4 = [9631]
No combination work for 5 cells
-> Either R7C4 = 7 or R1C4 = 9 -> R1C4 <> 7
7 of N2 locked in R13C6 -> not elsewhere in C6

R8 : 16 -> >= 2 cells
-> 10 <= R8C6
R8C12 <> 10, R8C123 <> 10 -> 10 locked in R8C2..6
-> 16 locked in R8C5..9
Since R8C5 = {24}, R8C6 = 1, R8C7 = {23} -> 16 must include R8C8 = 7
16 <> {178|457|2347}
-> 16 = R8C89 = [79] or R8C6..9 = [1375]
-> R8C9 = {59}
Since R8C7 = {23} -> 10 <> R8C3456 = {1234}
-> 10 = 2|3 cells <> {19|37|136}
-> 10 = R8C34 = [82] or R8C23 = [64] or R8C456 = [541]

8 of R8 locked in N7 -> not elsewhere in N7

R4 : 25 -> >= 4 cells -> must include R4C4 = 1
If R4C1..4 = 25 = {1789} -> R4C5 = 5, 8 = {26}
If R4C2..5 = 25 = {1789} -> 8 = {26}
If R4C1..5 = 25 = {12679} -> 8 = one cell
If R4C2..2 = 25 = {13569|13578} -> 8 = {8|26}
-> 8 = {8|26} locked in R4C789

C8:
Since R8C8 = 7 -> 7 = 2|3 cells -> bottom >= R4C8
-> top of 13 >= R6C8
Since R6C8 = {59} & R7C8 = {123} -> 13 <> R67C8 -> must include R8C8 = 7
-> 13 = {67} | {157}
Jean-Christophe

Posts: 149
Joined: 22 January 2006

Will try to map where you are Jean-Christophe to offer you advice - probably by PM. At the moment, I do not have a printed copy of the puzzle at home to write on but when I next get one I'll map your solution to your sticking point.

The only crucial Hanjie related "strategy" I think you need to use is to start marking squares whenever you can say they must be filled, or they must NOT BE filled. Both offer different kinds of information, but are critical to start defining where the actual cages are. Once you can pin down the cages, standard killer techniques emerge and will solve all of these puzzles. In the harder ones, you have to actually go back and forth between identifying cages and solving sudoku parts.

You'll need a notation that lets you mark used and unused cells and I prefer light shading for the used, and horizontal lines at the bottom of the unused cells. In both cases, I can still write the numbers in the boxes and read them without problem. As an alternative, people might try to print a second copy and put the "picture" on one, and the sudoku on the other.
Anyway, I know I made the later examples a bit hard but I hope you can make some more progress with them. This type ends up being very much a Killer sudoku with "mystery cages" and nicely combines killers with hanjie. I like it a lot and hope others try it out too.

In response to comerscroft, the link to my website with filled-in solutions (not walk-throughs) is in my original entry, but I will give the link to my general puzzles page where you can find this and other puzzles of mine:

motris

Posts: 71
Joined: 13 March 2006

Thanks for the tip.
Indeed I totally forgot the Hanjie crossed shaded/non shaded constraints (row & column intersections)
It make things much easier to solve.
Jean-Christophe

Posts: 149
Joined: 22 January 2006