# SudoCue - Sukaku

Suuji Kakure

This translates into: “The digits are hidden”. Following an ancient Japanese tradition, I will call it Sukaku.

### Introduction

A Sukaku puzzle has 81 groups of digits in a 9x9 grid. Like a standard Sudoku, you must complete the puzzle in such a way that each row, each column and each 3x3 box contains digits 1 through 9. You can only use the candidates shown in the grid. There are no given digits in a pure Sukaku. It is possible to create hybrid puzzles that have only a few given numbers, but I haven’t made them yet.

A Sukaku is more difficult than a Sudoku, because you have to solve all 81 cells with less information at your disposal. A given number in a Sudoku eliminates 28 candidates simultaneously. In a Sukaku, each of these candidates can be removed individually. This gives us a “fine tuning” method that is not available in a standard Sudoku. In fact, all possible Sudoku puzzles are only a small subset of all possible Sukaku puzzles.

Sukaku is not really a variant. It is a standard size Sudoku grid with no additional rules. You can use all the standard solving techniques for these puzzles. However, some techniques appear more often in Sukaku, like Hidden subsets and Empty Rectangles.

### Unsolvable?

Most computer solvers cannot handle puzzles without any given numbers. They will give an error message saying that the puzzle has no solution or has multiple solutions. This is not true. Every Sukaku on this website is guaranteed to have a single solution. Only SudoCue is capable of solving these puzzles.

### Sukaku Sample Puzzles

The following puzzle has a moderate level of difficulty - for a Sukaku.

If you want to use SudoCue to help you solve this puzzle, you need version 2.0.0.6 or higher. Earlier versions cannot handle grids without any clues. The following grid can be copied to the clipboard. You can then paste it into SudoCue.

```.------------------------------.------------------------------.------------------------------.
| 3459      12345789  45678    | 469       145789    12349    | 18        135789    13469    |
| 58        24569     14679    | 123469    1349      23479    | 123459    34689     45       |
| 1478      134789    235689   | 14679     24568     256      | 126       2568      24579    |
:------------------------------+------------------------------+------------------------------:
| 24589     1479      3478     | 1579      1459      1236     | 267       2789      14678    |
| 12458     2578      234578   | 12479     2379      145678   | 1456      36789     25679    |
| 12367     134689    479      | 1469      127       4578     | 2579      125689    13489    |
:------------------------------+------------------------------+------------------------------:
| 1345678   58        23458    | 235689    2689      123456789| 1345      1235789   2368     |
| 123789    24689     1389     | 246789    123579    34789    | 23678     134689    345689   |
| 24689     34589     268      | 1479      167       35678    | 146       14569     14       |
'------------------------------'------------------------------'------------------------------'
```

This Sukaku is an excellent training for Hidden Subsets and Empty Rectangles.

```.------------------------------.------------------------------.------------------------------.
| 123456789 3456789   13456789 | 1345678   1456789   123456789| 145789    123456789 123456789|
| 12345689  2345689   12345689 | 123456789 13458     12345689 | 124589    1234589   1234568  |
| 123456789 23456789  123456789| 13467     123456789 123456789| 1245789   123456789 12345678 |
:------------------------------+------------------------------+------------------------------:
| 123456789 3456789   3456789  | 35679     123456789 2345679  | 123456789 1345789   13456789 |
| 23456789  23456789  23456789 | 123456789 123456789 23456789 | 145789    1234789   123456789|
| 123456789 2345789   12345789 | 123456789 1245789   12345789 | 124789    1234789   123478   |
:------------------------------+------------------------------+------------------------------:
| 1234689   2346789   1234689  | 346789    123456789 34689    | 1246789   1234689   23468    |
| 123456789 23456789  123456789| 3456789   123456789 23456789 | 1456789   123456789 12345678 |
| 123456789 123456789 123456789| 13456789  13456789  123456789| 12456789  123456789 12345678 |
'------------------------------'------------------------------'------------------------------'
```

The following puzzle is also posted on the special page. Is it a relatively easy Sukaku.

```.---------------------------.---------------------------.---------------------------.
| 148      2467     3467    | 3569     23479    13      | 123569   13589    179     |
| 1236     12456789 1379    | 345      148      12589   | 1235689  234589   12468   |
| 3679     125      1459    | 1245789  4589     469     | 5678     237      258     |
:---------------------------+---------------------------+---------------------------:
| 1245     2579     1249    | 12567    3567     13568   | 1236     13456789 1467    |
| 245      2568     34      | 3456     45789    247     | 13       135      23489   |
| 138      1368     13479   | 12345679 45689    126     | 1234789  14678    569     |
:---------------------------+---------------------------+---------------------------:
| 49       12469    1248    | 234      1234578  356     | 24569    2678     12458   |
| 346789   348      389     | 234569   567      469     | 156      1379     126     |
| 125689   23579    13456   | 38       12357    379     | 1248     238      23      |
'---------------------------'---------------------------'---------------------------'
```

Use the forum or the comment form if you want to play Sukaku on a regular basis. I do have a modest collection of Sukakus available.

### Sukaku Records

There are several known records for Sudoku. The minimum number of given numbers for a unique solution is 17. The maximum number of givens for a minimal Sudoku is 34. As soon as I introduced Sukaku grids, questions were asked about the limits. So I started some searches. These are the results.

#### Lowest number of candidates

81. But that is no puzzle. 82 maybe? Too easy. A minimum of 162 candidates would be required to avoid all naked singles. However, it is not possible to make a grid with 162 candidates that has no hidden singles. I have not yet investigated how many candidates are needed to avoid all hidden singles.

#### Highest number of candidates

The current record is 633. This record was established at October 27, 2006. You can solve this remarkable puzzle with simple techniques.

```.------------------------------.------------------------------.------------------------------.
| 123456789 2356789   123456789| 1235679   12356789  123456789| 12456789  1245789   123456789|
| 123456789 123456789 12456789 | 135679    123456789 123456789| 12456789  15789     12456789 |
| 134567    23456789  12456789 | 1345679   123456789 123456789| 12456789  145789    12456789 |
:------------------------------+------------------------------+------------------------------:
| 12456789  123456789 2456789  | 135679    12356789  12356789 | 1245679   13579     1235679  |
| 3456789   3456789   456789   | 12345679  12356789  123456789| 123456789 123456789 12345679 |
| 2456789   256789    2456789  | 123456789 1256789   123456789| 12456789  12345789  123456789|
:------------------------------+------------------------------+------------------------------:
| 12346789  236789    246789   | 12345679  1256789   2346789  | 12456789  12456789  123456789|
| 12346789  123456789 12456789 | 1345679   123456789 123456789| 1456789   123456789 12345689 |
| 123456789 2356789   123456789| 1345679   123456789 123456789| 123456789 134589    12345689 |
'------------------------------'------------------------------'------------------------------'
```

Here is the runner-up with 631 candidates.

```.------------------------------.------------------------------.------------------------------.
| 1246789   1245789   1456789  | 1245679   12456789  12456789 | 12456789  123456789 12456789 |
| 1236789   2356789   12356789 | 125679    123456789 2356789  | 12356789  2356789   2356789  |
| 12346789  12345789  123456789| 1245679   123456789 23456789 | 123456789 23456789  23456789 |
:------------------------------+------------------------------+------------------------------:
| 123456789 125789    125689   | 123456789 123456789 123456789| 1245689   12356789  123456789|
| 123456789 12345789  123456789| 12345679  123456789 23456789 | 123456789 123456789 123456789|
| 12346789  123456789 123456789| 12345679  123456789 378      | 123456789 23456789  123456789|
:------------------------------+------------------------------+------------------------------:
| 123456789 12456789  12456789 | 12346789  123456789 2346789  | 245689    23456789  23456789 |
| 123456789 123456789 1245689  | 12469     124689    12346789 | 123456789 234589    234589   |
| 123456789 2345789   23456789 | 24679     2346789   2346789  | 2345789   2345789   2345789  |
'------------------------------'------------------------------'------------------------------'
```

#### Hardest Sukaku Puzzle

Define “hard”. An objective measurement is the backdoor size. This is the number of subsequent lucky guesses that you need to make to solve the puzzle with easy techniques. For singles only, the record puzzle has 2 backdoors of size 3, sharing the same 2 cells. Here it is, the hardest Sukaku so far:

```.------------------------.------------------------.------------------------.
| 1237    1256    36789  | 25789   4789    4569   | 1679    23457   1348   |
| 2456    13489   3459   | 1356    3679    1247   | 2478    5789    12368  |
| 2358    24789   1267   | 2489    123457  13468  | 34569   4568    1279   |
:------------------------+------------------------+------------------------:
| 1569    2578    3457   | 145678  3459    2356   | 234689  1236    146789 |
| 3679    12348   2489   | 1236    56789   1569   | 2357    1489    4579   |
| 14689   1567    234678 | 1237    12489   34578  | 1235    5789    6789   |
:------------------------+------------------------+------------------------:
| 24789   3678    1469   | 1346    1246    1357   | 5689    1256789 2345   |
| 1238    4569    125678 | 3579    2347    2689   | 1479    1348    2356   |
| 3457    3789    1256   | 23489   14568   256789 | 1578    23569   1457   |
'------------------------'------------------------'------------------------'
```