# Number In Order

Number In Order Example

Number In Order is a puzzle original to this blog to the best of my knowledge. This puzzle genre is inspired from str8ts, which is made by Jeff Widderich.

Cell types

Similar to str8ts, a cell is either black (gray) or white. In an unsolved puzzle, some white cells are blank while the others are filled with numbers. To solve the puzzle, the white cells must be all filled with some numbers to satisfy a rule.

Interaction

First, define a “run of cells” to be some white cells in the same row or column such that they are all adjacent to each other, and they can’t be expanded (either by being blocked by a black cell or the edge of the grid). So, R3C1 and R3C2 is a run of 2 cells. R3C4 is a run of 1 cell, separate from R3C1 and R3C2. Let’s define the length of the longest run of cells to be x.

All the numbers in a run of cells must be consecutive integers. Moreover, each cell may only contain a number between 1 and x, inclusive. So the longest run of cells will have all the numbers from 1 to x. This effectively also stops a run of cells to have duplicate numbers.

Objective

Fill each cell with a number to satisfy the above conditions.

Walkthrough of the example

Note the R2C3-R2C4 run. R2C3 is 1, and R2C3 and R2C4 must be consecutive positive integers. So R2C4 is 2. This also makes R1C3, R3C1, and R4C2 be 2 too, since the longest run of cells is 3, not 4.

The rest are runs of three cells, which must contain all numbers from 1 to 3. Simply use the usual Latin Squares technique and the puzzle is solved.

### 18 Responses to Number In Order

1. The addition of black cells with white numbers is what makes this puzzle shine. Minimum number combination should be from 1 to 6, then it is worthwhile. This is Str8ts not Number In Order really bad name for a puzzle.

Also, you have a list of all the famous puzzles, please refer to this puzzle as Str8ts not Number In Order.

• chaotic_iak says:

This puzzle has more distinctions than what I would call a variation of Str8ts.

2. You are kidding right!
You start this post with this sentence
“Number In Order is a puzzle original to this blog”
The concept of Str8ts is an inventors dream come true. The concept is a perfect constant. The concept always standsalone making variations next to impossible.
No idea what distinctions you are refering to, as far as I can see there are none.

• chaotic_iak says:

1. A row or a column doesn’t need to have all different numbers as Str8ts do. The example already shows that.
2. The maximum number in a grid is determined by the length of the longest run of white cells in a row/column, unlike Str8ts which is determined by the size of the board.
3. I got the idea myself, not depending on Str8ts (although after some research I find out that it’s pretty similar).

Reasons 1 and 2 makes the solving method different; in some cases drastically.

Also another reason that Number In Order deserves its own name: see Star Slitherlink, Sheep and Wolves, No-Square Slitherlink, Mirror Akari, Fillomino Connection. They have their own names due to the addition of a variation that makes their solving different than the original (okay, scratch a few, but there’s still enough to support).

3. 1. Str8ts doesn’t need to have all numbers present in a row or column! Numbers are always missing. Do your homework before you make such comments.
2. The puzzle you are showing doesn’t even make any sense. In reference to point 2.

• chaotic_iak says:

1. I said all different numbers, not all numbers. In my example puzzle above, row 3 repeats 3. In Str8ts, a number cannot appear more than once in a row/column.
2. Because it’s not Str8ts. It’s Number In Order. Str8ts’ maximum number is always 9 in a 9×9 puzzle, while Number In Order’s maximum number is almost always not 9 (depends on the puzzle) even in a 9×9 puzzle.

4. The puzzle you have created makes absolutely no logical sense. It isn’t worth solving. The addition of duplicate numbers in rows and columns basically ruins the purity of the puzzle. The entire exercise looks like you tried to make Str8ts different. The problem is Str8ts mechanically can’t be altered or improved. I have tried all possible scenarios. The puzzle simply is based on a super simple mechanisum that is perfect the way it is.

• chaotic_iak says:

I’ve said that I got the inspiration without knowing Str8ts; only after I made this genre that I did some research and found out that it’s similar to Str8ts. As it’s my invented genre, I can do anything to it. Ruining the purity or something doesn’t make me necessarily stop Number In Order and use Str8ts instead.

5. Having duplicate numbers in rows and columns kills the puzzle. It opens up millions of possiblities for puzzles larger than 1 to 6. You run a puzzle blog and you never bounced into Str8ts come on.
Then you change the only things that can be changed to Str8ts. No logical person would invent your version, they would have come up with Str8ts. Why introduce a rule that allows the use of the same numbers when you could make them unique.
chaotic__iak I am not trying to give you a hard time it is just that your story makes absolutely no sense.

• MellowMelon says:

“You run a puzzle blog and you never bounced into Str8ts come on.”
That’s perfectly understandable. Where would a fan of quality logic puzzles be expected to run into Str8ts?

“chaotic__iak I am not trying to give you a hard time…”
Really? Then what are you trying to do?

6. MellowMelon,
You are right but this kind of stuff really ticks me off. Especially when nothing makes any sense.

• chaotic_iak says:

Even if nothing makes sense, it’s my puzzle. My own invented puzzle genre. It has no bearing with Str8ts, and it’s up to me whether I want it to have weird/nonsense rules in one’s opinion.

7. Puzzles are based on logic. This is a puzzle blog. So here is the discussion….

Adding the option of duplicate numbers in a row or column might work on a puzzle that uses digits from 1 to 3. That is about it though. If for example you add this option on a 9 x 9 grid the puzzle is unsolvable and will probably have more than 10 million possible solutions instead of the coveted single solution the puzzle needs.

So yes this puzzle belongs to you. Number in Order doesn’t work. It is not a puzzle. The math is black and white. That is the reason I am discussing the issue.

8. Well i like the puzzle a lot.
I know how you feel Choatic, I made a awesome puzzle and called it a chimera and was all happy…
until I realized mellow mellon already had made something very very similar called the loop of death.

9. Elolo,

How can you like Number in Order when it could never be used to generate a single puzzle. Allowing duplicate numbers in rows and columns makes the puzzle impossible to solve. That is the exact reason why chaotik iak made his sample using 1 to 3. Even with 1 to 4 it falls apart.

Come on guys you are puzzle makers you know the math doesn’t work. That is what make puzzles so tough, either the math works or it doesn’t. This Number in Order doesn’t work way too many possibilities and a puzzle larger than 3 x 3 would have way too many solutions. Sorry

10. chaotic_iak says:

I made a valid and nontrivial 8×8 Number In Order with numbers from 1 to 8. If you don’t know where it is, you shouldn’t even comment on a blog that you don’t want to read carefully.

11. Checked out your 1 to 8 version. You confirmed everything that I stated. The puzzle has endless solutions because of your rule allowing duplicate numbers in rows and columns.
If we would run this through our solver I would estimate several thousand possible solutions.
In row 8 I can see multiple different ways of filling in that row alone (just as an example)
Number in Order doesn’t work. The math doesn’t work!
Another big issue is a person solving this will never feel confirmation that they are on the right track during a solve. Meaning they are unable to feel comfortable while cross checking their on going solution. They will immediately be doubting their progress. Not a good thing.

Sorry Chaotic_iak the math unfortunately never lies.

12. chaotic_iak says:

Wrong; it is perfectly valid and I have checked it. You forgot that a run of cells must have consecutive numbers, not only distinct numbers.