Blue Clouds - Dekadoku

Question

I greatly appreciate your support in this new challenge. I want to share this puzzle with you and hear your thoughts on the new rule I've added. What do you think? Thank you in advance for your feedback.

The rules are the same as before, but with one additional rule:

1. Fill the grid with all combinations of two-digit numbers (from 00 to 99).
2. In each row or column, no number can have the same tens digit.
3. In each row or column, no number can have the same units digit.
4. No consecutive numbers are allowed either vertically, horizontally, or diagonally.

Previous posts:

A new nameless game

DEKADOKU, the new challenge

Text version:

   85 60    14 59    76 33
73       57       96       11
38       69       55       82
   79 87    98 34    52 16
54       02       31       78
40       74       83       95
   92 58    81 70    03 27
22       13       68       50
89       90       77       36
   30 93    72 65    48 51

Answer 1

Another lovely puzzle, thanks for making them!

Here's the solution:

For feedback:

I like the concept of no consecutive numbers a lot, however in practice I didn't use the restriction once to solve, and instead just used the normal rules. I think the puzzle would have to be harder and have a lot less numbers for it to come into use, and even then it would be a rare case.

However if a puzzle can be made where the restriction is necessary to solve, I think that would be very interesting and tricky!

---

Step by step:

1:

It makes sense to focus on the columns and rows with only 4 cells remaining, so let's do that.

In the top row, the tenth cell must end in 7, whilst the 7th must end in 2, the 4th must end in 8, and the first in 1.

In fact, the 4th cell can only be 28, the seventh must be 42. This solves the top row, placing 07 and 91 as well.

In the first column now, 91 means the 4th cell must be 05, the 7th must be 66, and the tenth must be 17.

2:

Lets continue checking each of the 4 columns with 4 cells.

The 4th column must have 41 in its 4th cell now, leaving 86 in the tenth cell and leaving 35 in the 7th.

The 7th column can also be solved now, as there must be 20 in the 4th cell, 19 in the 7th and 04 in the tenth.

And unsurprisingly, the tenth column can also be solved, with 63, 44 and 29.

3:

Now lets start on the sub sections, and these will be harder. As each cell has 6 possibilities per row and column in these sections, at best there will be 2 candidate digits left when comparing - so there won't be any obvious single cells left over.

In fact, let's calculate all the candidates to help us:



As expected, there is nothing immediately obvious here and we'll have to get a bit more crafty.

4:

Towards the top middle, there is a cell with candidates 0248|28. However, as 02, 22, 42 and 82 are all taken already, it must end in 8, and can only be 08 or 88.

This means in the top left, the cell must end in 4, and can be 24 or 64.

In the 3rd row, as 70 and 74 are taken, the 7- cannot be in the final free cell, and can only be in one cell. The final two 7-s can actually be placed because of this:

5:

56 must be in one of 2 cells in row 6, so clashing candidates can be removed, and the same for 53 in row 9.

In the 9th column, as 42, 44 and 48 are all taken, the bottom right free cell can have 4 removed as a 4- candidate. This leaves a 06 pair in that column, meaning the 09|04 further up must start with 9, and hence must be 94.

The cell to the left of 94 must now be 10, as 17, 20 and 27 are taken.

There is also a 236 triple for the leading digit in the 8th column which can simplify other cells. In fact the fifth cell must now start with 9, leaving the other simplified cell to have to be 84.

6:

There is only one place for -2 in the second row, and it actually must be 32. This resolves a 25 in the same row, solving the 26|4 as 64 too.

32 also solves an 09 in the third column, also placing a 46. In fact, this entire column can be resolved, with 15 and 24.

7:

The 24 resolves a 61 in it's row. 08 can be placed right next to it, which means the 08|8 from earlier must be 88. Back to the 9th row though, and 12 can also be placed.

In the 9th column, 08 means a 62 can be placed, and in the second row, the 88 resolves the 48|09 as 49, which then solves the 9th column.

The second row has one number left that can also be filled in as 00.

8:

Finally, in the 8th row, the 9- must be 97, and the row can be resolved. This also resolves the 8th column.

The 9th row can be solved as the second free cell must be 45.

There are now just 9 cells left.

There is only one 0- left, 06, so this can be placed, and the same for the last 2-, 21.

The last 1-, 18, can now be placed, followed by 56 in the same row. 43 can be placed in column 6, and the last 4 cells resolve themselves to give the solution: