# Kakurosities

### Kakuro's younger brothers

Simpler versions of Kakuro can be obtained by tweaking the first
rule. **Katrio** has the rule that you can use only the digits 1 and 2. Then
the only number which has a partition is $3\; (=1+2)$. This
is the only clue that you can have. Not only is Katrio a bit of a bore,
it is not even unique (unless you decide to allow partitions into single
numbers: $1=1$ and $2=2$). **Kabin** passed away
early, mourned by the siblings. What is a puzzle to do
when it is born with a rule that says use only 1 and that
too not more than once?

Kaquadro allows the digits 1, 2 and 3. The allowed clues are 3, 4, 5 and 6. Simple, you say? But did you realize that Kaquadro puzzles can be as large as you wish? Nevertheless you are right. One can prove that Kaquadro is in P and not in NP.

Kapenta,
**Kahex**, **Kasept**, **Kocho** and **Kanona**
are part of the mocktail circuit, although
Kapenta cannot shake off a feeling that Kakuro is twice as lively.
The older siblings are stratospheric. Even **Kundici** has not been
spotted in public in the memory of any of the youngsters.

### Kakuro's cousins

The cousins of Kakuro are obtained by tweaking the second rule. **Twokuro**
demands that each number be allowed exactly twice in each partition. The
clues would then have to be even numbers. My friend Simplicio believes
that Twokuro gives itself airs: every Twokuro can be exactly transcribed
into a Kakuro. I notice that Sagredo is sitting off in one corner with his
laptop and not rising to the bait. Perhaps he thinks Simplicio is wrong again?

### Monotonic Kakuro

Adding extra rules simplifies Kakuro. A third rule could be added: that the digits which solve a clue must be written in increasing order along the row or column. With this rule 3=1+2 is allowed, but not 3=2+1. Call this Ascending Kakuro. One could also have Descending Kakuro, in which the solution must have digits written in decreasing order. Ascending and descending Kakuro are two members of the family of Monotonic Kakuro. A moment's thought will assure you that these are simpler than Kakuro. But how simple? Can you look at a puzzle and decide whether it belongs to Monotonic Kakuro rather than Kakuro?

© Sourendu Gupta. Mail me if you want to reproduce any part of this page. My mailing address is a simple (satisfactory) puzzle for you to solve. Created on 30 November, 2006. Last modified on 4 December, 2006.