## Introducing KakuroZero

For fans of Kakuro

### Introducing KakuroZero

These puzzles are a variation of standard Kakuro, with digit values in the range 0 to 9. This simple change offers a higher potential level of complexity.

For example, a run length of 4 with sum 10 is no longer unique, since we can have any of:
• 0 1 2 7
• 0 1 3 6
• 0 1 4 5
• 0 2 3 5
• 1 2 3 4

Here is a simple example to begin with:
Attachments
KZ_Example1.jpg (41.17 KiB) Viewed 1083 times

Mathimagics
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Location: Canberra

### Introducing KakuroZero

And here is a slightly harder example:
Attachments
KZ_Example2.jpg (41.9 KiB) Viewed 1082 times

Mathimagics
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Posts: 1762
Joined: 27 May 2015
Location: Canberra

### Introducing KakuroZero

Here are the solutions to the examples above:
Example1:
Hidden Text: Show
013x01x
1460253
x391x20
968x041
10x210x
8519230
x20x361

Example2:
Hidden Text: Show
142x45x
2891043
x762x20
968x091
52x410x
7503261
x93x485

Mathimagics
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Joined: 27 May 2015
Location: Canberra

### KakuroZero - a larger sample

Here is one for the more adventurous:

KZ_Example3E.jpg (70.78 KiB) Viewed 1072 times

Solution:
Hidden Text: Show
451xxxx089
8924xx0135
9758xx1468
6803415297
xxx6839xxx
xxx1203xxx
1630927458
2945xx4316
0512xx2107
789xxxx789

Mathimagics
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Posts: 1762
Joined: 27 May 2015
Location: Canberra

### Re: Introducing KakuroZero

How about Hexadecimal Zeroes-Allowed Kakuro? Allowable values would be 0-9 and A-F.

In keeping with the spirit, sums (clues) should be given in hexadecimal, as well.

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

### KakuroH?

Why not indeed? As you may know, I have been experimenting with various grid sizes in order to determine the maximum number of blank cells NB for which unique solutions exist.

I had intended to generalise this to explore the effect of various domain sizes, D. Standard Kakuro has D = 9, KakuroZero is really standard Kakuro with D = 10, KakuroHex would be D = 16.

The expected effect is a reduction in max NB for increasing D, and vice-versa.

My original software was developed in my usual slap-dash manner, and it assumed D = 9. This made KZ a little tricky to arrive at, but now I have sorted that out, I should be able to to produce puzzles for arbitrary D without too much trouble.

Mathimagics
2017 Supporter

Posts: 1762
Joined: 27 May 2015
Location: Canberra

### KakuroHex sample

Ok, it seems be working.

I have attached two samples, one with clues are shown in decimal, and a different puzzle with clues in hex.

I am not convinced hex-clues is really a good idea, on reflection.

First you have to convert them, which is not an issue, but you then have to either mark the decimal values into the grid, thus making a potential mess, or else keep a list separately, and thus lose the direct visual clue/sum correspondence.

Anyway, you be the judge!

I do provide the solutions in hex format, since this allows a single-character for each position, and will do this for D <= 36 (heaven forbid I ever venture that far!).

Clues in normal (decimal) format
KP080816_Test168D.jpg (43.7 KiB) Viewed 1043 times

Solution (Test168D):
Hidden Text: Show
023x01x
54E0162
xFD3x40
401xFD9
F7xC32x
8324501
x10xC32

Clues in HEX format
KP080816_Test128H.jpg (43.23 KiB) Viewed 1043 times

Solution (Test128H):
Hidden Text: Show
20Bx05x
0563142
x2A0x31
013xFD8
F6xF72x
2473901
x30x014

Mathimagics
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Posts: 1762
Joined: 27 May 2015
Location: Canberra

Mathimagics wrote:

---KakuroZero is really standard Kakuro with D = 10

or D=10 could be 1-9 + A

Pat

Posts: 3904
Joined: 18 July 2005

### Re: Introducing KakuroZero

Yes, it could be that way.

But I have decided to adopt the convention that for D <= 9, the value range will be {1, 2, ... D}, and for D > 9 the range will be {0, 1, ... D-1}.

Mathimagics
2017 Supporter

Posts: 1762
Joined: 27 May 2015
Location: Canberra

### KakuroHex samples

Here are two KauroHex samples on a larger grid. Cell values are 0 to 15.

The second example is harder than the first.

KP111116_Test001.jpg (71.63 KiB) Viewed 1035 times

Solution (KP111116_Test001)
Hidden Text: Show
0D1xxxx0E1
EF9DxxEAF2
CEABF298D0
x63470215x
xx09xxC7xx
xx7CxxFDxx
x28F01B34x
F3DE49ABC2
102AxxDEFB
E16xxxx290

KP111116_Test064R.jpg (71.97 KiB) Viewed 1035 times

Solution (KP111116_Test064R)
Hidden Text: Show
62ExxxxFAE
1062xx1508
31540D672F
x4C8DF9E6x
xxFDxx38xx
xx93xx02xx
xD70EF4C6x
0B216D5437
8FDCxx2104
1EBxxxxDCF

Mathimagics
2017 Supporter

Posts: 1762
Joined: 27 May 2015
Location: Canberra