*Even more so, since I can't use a pencil and eraser on my PC.*The books are good value, 128 puzzles at about 20c each ().

That'd certainly be an interesting step to add them. Do you first generate a grid of back cells and then try to find sums fitting them?

I think you could have a database of already generated puzzles (like atk),with a classification corresponding to the result of generation (and not to a max allowed during the generation process - a max that, most of the time, cannot be effectively reached by the result, for statistical reasons).

one with a unique solution) are infinitesmal for any decent grid size.

For example, just with a small grid of 10x10, I ran the naive-model random generator for several hours without even coming close to unqueness! However, based on the way top-down Sudoku generators work, I imagine all the generators start by choosing grid size, then pattern of black/white cells ...

My current benchmark standard is Conceptis's "Absolutely Nasty Kakuro - Level 4". Unlike Sudoku., I wanted to try the commercial website you mention, but only a few "easy" or "very easy" puzzles are available unless you register.

Could you post one of those you consider as typical of "Absolutely Nasty Kakuro - Level 4"? However, based on the way top-down Sudoku generators work, I imagine all the generators start by choosing grid size, then pattern of black/white cells (often making it nice looking in some sense and/or with some symmetries), then (more or less randomly) fill the white grid, then compute the sums in the black cells, and then delete sums one by one as long as unicity is preserved.This example is puzzle #103: 24 rows 14 cols 0[[

Could you post one of those you consider as typical of "Absolutely Nasty Kakuro - Level 4"? However, based on the way top-down Sudoku generators work, I imagine all the generators start by choosing grid size, then pattern of black/white cells (often making it nice looking in some sense and/or with some symmetries), then (more or less randomly) fill the white grid, then compute the sums in the black cells, and then delete sums one by one as long as unicity is preserved.

This example is puzzle #103: 24 rows 14 cols 0\0 0\0 30\0 45\0 35\0 37\0 6\0 21\0 24\0 0\0 35\0 17\0 42\0 28\0 0\0 16\42 - - - - - - - 0\29 - - - - 0\36 - - - - - - - - 4\19 - - - - 0\35 - - - - - 30\20 - - - - 35\15 - - 0\28 - - - - - - - 17\26 - - - - - 0\0 17\0 29\39 - - - - - - 37\21 - - - - 0\19 - - - 11\22 - - - - - 19\9 - - - 0\32 - - - - - - 45\33 - - - - - - 0\0 27\23 - - - - 16\16 - - - - - 4\0 11\0 0\29 - - - - 7\29 - - - - - 30\3 - - 0\14 - - 13\0 0\7 - - - 15\30 - - - - - 0\20 - - - 0\33 - - - - - - - 29\0 30\0 0\8 - - - 17\0 24\7 - - - 4\0 0\21 - - - 0\0 3\0 11\42 - - - - - - - 0\23 - - - 0\18 - - - - - 21\7 - - - 11\0 45\13 - - 0\4 - - 35\16 - - - - - 44\27 - - - - 0\0 29\0 41\27 - - - - - 10\23 - - - - 6\0 0\39 - - - - - - 39\21 - - - - - - 0\11 - - - 32\24 - - - - - 35\10 - - - 0\30 - - - - 15\33 - - - - - - 22\0 10\0 0\34 - - - - - 22\28 - - - - - - - 0\3 - - 17\22 - - - - 15\33 - - - - - 0\28 - - - - 0\36 - - - - - - - - 0\22 - - - - 0\31 - - - - - - - 0\0 However, based on the way top-down Sudoku generators work, I imagine all the generators start by choosing grid size, then pattern of black/white cells ...

then (more or less randomly) fill the white grid, then compute the sums in the black cells, and then delete sums one by one as long as unicity is preserved. I use just that method for generating Skyscraper puzzles, which was my first venture into puzzle-creating software.

I think this process is somewhat akin to what Conceptis uses for their kakuro books, at least, their puzzles and mine have lots of similar attributes.

Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Could you post one of those you consider as typical of "Absolutely Nasty Kakuro - Level 4"? However, based on the way top-down Sudoku generators work, I imagine all the generators start by choosing grid size, then pattern of black/white cells (often making it nice looking in some sense and/or with some symmetries), then (more or less randomly) fill the white grid, then compute the sums in the black cells, and then delete sums one by one as long as unicity is preserved.This example is puzzle #103: 24 rows 14 cols 0\0 0\0 30\0 45\0 35\0 37\0 6\0 21\0 24\0 0\0 35\0 17\0 42\0 28\0 0\0 16\42 - - - - - - - 0\29 - - - - 0\36 - - - - - - - - 4\19 - - - - 0\35 - - - - - 30\20 - - - - 35\15 - - 0\28 - - - - - - - 17\26 - - - - - 0\0 17\0 29\39 - - - - - - 37\21 - - - - 0\19 - - - 11\22 - - - - - 19\9 - - - 0\32 - - - - - - 45\33 - - - - - - 0\0 27\23 - - - - 16\16 - - - - - 4\0 11\0 0\29 - - - - 7\29 - - - - - 30\3 - - 0\14 - - 13\0 0\7 - - - 15\30 - - - - - 0\20 - - - 0\33 - - - - - - - 29\0 30\0 0\8 - - - 17\0 24\7 - - - 4\0 0\21 - - - 0\0 3\0 11\42 - - - - - - - 0\23 - - - 0\18 - - - - - 21\7 - - - 11\0 45\13 - - 0\4 - - 35\16 - - - - - 44\27 - - - - 0\0 29\0 41\27 - - - - - 10\23 - - - - 6\0 0\39 - - - - - - 39\21 - - - - - - 0\11 - - - 32\24 - - - - - 35\10 - - - 0\30 - - - - 15\33 - - - - - - 22\0 10\0 0\34 - - - - - 22\28 - - - - - - - 0\3 - - 17\22 - - - - 15\33 - - - - - 0\28 - - - - 0\36 - - - - - - - - 0\22 - - - - 0\31 - - - - - - - 0\0 However, based on the way top-down Sudoku generators work, I imagine all the generators start by choosing grid size, then pattern of black/white cells ...then (more or less randomly) fill the white grid, then compute the sums in the black cells, and then delete sums one by one as long as unicity is preserved. I use just that method for generating Skyscraper puzzles, which was my first venture into puzzle-creating software.I think this process is somewhat akin to what Conceptis uses for their kakuro books, at least, their puzzles and mine have lots of similar attributes.Including the fact their hards and my hards aren't very hard for a seasoned solver.I liked the idea of every solve iteration having at least one solution, so it wouldn't waste its time with totally unsolvable puzzles.The solver is coded so that if a puzzle has multiple solutions it will fail to find any of them.It'd also be nice to have the puzzles named some way, so that we can refer to them without having to post them. to what Conceptis uses for their kakuro books, at least, their puzzles and mine have lots of similar attributes.Including the fact their hards and my hards aren't very hard for a seasoned solver. I am also trying to develop Kakuro generating software, and am also familiar with Conceptis puzzles. PS: You must have also noticed, as I have, how very little information about puzzle-generation there is available in the public domain.Although maybe that's just me being bad at kakuros. I'd also love to hear a good algorithm for detecting naked triples!As most of your puzzles have obvious surface sums, it's strange that you don't use them.

]] 0[[Could you post one of those you consider as typical of "Absolutely Nasty Kakuro - Level 4"? However, based on the way top-down Sudoku generators work, I imagine all the generators start by choosing grid size, then pattern of black/white cells (often making it nice looking in some sense and/or with some symmetries), then (more or less randomly) fill the white grid, then compute the sums in the black cells, and then delete sums one by one as long as unicity is preserved.

This example is puzzle #103: 24 rows 14 cols 0\0 0\0 30\0 45\0 35\0 37\0 6\0 21\0 24\0 0\0 35\0 17\0 42\0 28\0 0\0 16\42 - - - - - - - 0\29 - - - - 0\36 - - - - - - - - 4\19 - - - - 0\35 - - - - - 30\20 - - - - 35\15 - - 0\28 - - - - - - - 17\26 - - - - - 0\0 17\0 29\39 - - - - - - 37\21 - - - - 0\19 - - - 11\22 - - - - - 19\9 - - - 0\32 - - - - - - 45\33 - - - - - - 0\0 27\23 - - - - 16\16 - - - - - 4\0 11\0 0\29 - - - - 7\29 - - - - - 30\3 - - 0\14 - - 13\0 0\7 - - - 15\30 - - - - - 0\20 - - - 0\33 - - - - - - - 29\0 30\0 0\8 - - - 17\0 24\7 - - - 4\0 0\21 - - - 0\0 3\0 11\42 - - - - - - - 0\23 - - - 0\18 - - - - - 21\7 - - - 11\0 45\13 - - 0\4 - - 35\16 - - - - - 44\27 - - - - 0\0 29\0 41\27 - - - - - 10\23 - - - - 6\0 0\39 - - - - - - 39\21 - - - - - - 0\11 - - - 32\24 - - - - - 35\10 - - - 0\30 - - - - 15\33 - - - - - - 22\0 10\0 0\34 - - - - - 22\28 - - - - - - - 0\3 - - 17\22 - - - - 15\33 - - - - - 0\28 - - - - 0\36 - - - - - - - - 0\22 - - - - 0\31 - - - - - - - 0\0 However, based on the way top-down Sudoku generators work, I imagine all the generators start by choosing grid size, then pattern of black/white cells ...

then (more or less randomly) fill the white grid, then compute the sums in the black cells, and then delete sums one by one as long as unicity is preserved. I use just that method for generating Skyscraper puzzles, which was my first venture into puzzle-creating software.

I think this process is somewhat akin to what Conceptis uses for their kakuro books, at least, their puzzles and mine have lots of similar attributes.

Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Could you post one of those you consider as typical of "Absolutely Nasty Kakuro - Level 4"? However, based on the way top-down Sudoku generators work, I imagine all the generators start by choosing grid size, then pattern of black/white cells (often making it nice looking in some sense and/or with some symmetries), then (more or less randomly) fill the white grid, then compute the sums in the black cells, and then delete sums one by one as long as unicity is preserved.This example is puzzle #103: 24 rows 14 cols 0\0 0\0 30\0 45\0 35\0 37\0 6\0 21\0 24\0 0\0 35\0 17\0 42\0 28\0 0\0 16\42 - - - - - - - 0\29 - - - - 0\36 - - - - - - - - 4\19 - - - - 0\35 - - - - - 30\20 - - - - 35\15 - - 0\28 - - - - - - - 17\26 - - - - - 0\0 17\0 29\39 - - - - - - 37\21 - - - - 0\19 - - - 11\22 - - - - - 19\9 - - - 0\32 - - - - - - 45\33 - - - - - - 0\0 27\23 - - - - 16\16 - - - - - 4\0 11\0 0\29 - - - - 7\29 - - - - - 30\3 - - 0\14 - - 13\0 0\7 - - - 15\30 - - - - - 0\20 - - - 0\33 - - - - - - - 29\0 30\0 0\8 - - - 17\0 24\7 - - - 4\0 0\21 - - - 0\0 3\0 11\42 - - - - - - - 0\23 - - - 0\18 - - - - - 21\7 - - - 11\0 45\13 - - 0\4 - - 35\16 - - - - - 44\27 - - - - 0\0 29\0 41\27 - - - - - 10\23 - - - - 6\0 0\39 - - - - - - 39\21 - - - - - - 0\11 - - - 32\24 - - - - - 35\10 - - - 0\30 - - - - 15\33 - - - - - - 22\0 10\0 0\34 - - - - - 22\28 - - - - - - - 0\3 - - 17\22 - - - - 15\33 - - - - - 0\28 - - - - 0\36 - - - - - - - - 0\22 - - - - 0\31 - - - - - - - 0\0 However, based on the way top-down Sudoku generators work, I imagine all the generators start by choosing grid size, then pattern of black/white cells ...then (more or less randomly) fill the white grid, then compute the sums in the black cells, and then delete sums one by one as long as unicity is preserved. I use just that method for generating Skyscraper puzzles, which was my first venture into puzzle-creating software.I think this process is somewhat akin to what Conceptis uses for their kakuro books, at least, their puzzles and mine have lots of similar attributes.Including the fact their hards and my hards aren't very hard for a seasoned solver.I liked the idea of every solve iteration having at least one solution, so it wouldn't waste its time with totally unsolvable puzzles.The solver is coded so that if a puzzle has multiple solutions it will fail to find any of them.It'd also be nice to have the puzzles named some way, so that we can refer to them without having to post them. to what Conceptis uses for their kakuro books, at least, their puzzles and mine have lots of similar attributes.Including the fact their hards and my hards aren't very hard for a seasoned solver. I am also trying to develop Kakuro generating software, and am also familiar with Conceptis puzzles. PS: You must have also noticed, as I have, how very little information about puzzle-generation there is available in the public domain.Although maybe that's just me being bad at kakuros. I'd also love to hear a good algorithm for detecting naked triples!As most of your puzzles have obvious surface sums, it's strange that you don't use them.

]] 30[[Could you post one of those you consider as typical of "Absolutely Nasty Kakuro - Level 4"? However, based on the way top-down Sudoku generators work, I imagine all the generators start by choosing grid size, then pattern of black/white cells (often making it nice looking in some sense and/or with some symmetries), then (more or less randomly) fill the white grid, then compute the sums in the black cells, and then delete sums one by one as long as unicity is preserved.

This example is puzzle #103: 24 rows 14 cols 0\0 0\0 30\0 45\0 35\0 37\0 6\0 21\0 24\0 0\0 35\0 17\0 42\0 28\0 0\0 16\42 - - - - - - - 0\29 - - - - 0\36 - - - - - - - - 4\19 - - - - 0\35 - - - - - 30\20 - - - - 35\15 - - 0\28 - - - - - - - 17\26 - - - - - 0\0 17\0 29\39 - - - - - - 37\21 - - - - 0\19 - - - 11\22 - - - - - 19\9 - - - 0\32 - - - - - - 45\33 - - - - - - 0\0 27\23 - - - - 16\16 - - - - - 4\0 11\0 0\29 - - - - 7\29 - - - - - 30\3 - - 0\14 - - 13\0 0\7 - - - 15\30 - - - - - 0\20 - - - 0\33 - - - - - - - 29\0 30\0 0\8 - - - 17\0 24\7 - - - 4\0 0\21 - - - 0\0 3\0 11\42 - - - - - - - 0\23 - - - 0\18 - - - - - 21\7 - - - 11\0 45\13 - - 0\4 - - 35\16 - - - - - 44\27 - - - - 0\0 29\0 41\27 - - - - - 10\23 - - - - 6\0 0\39 - - - - - - 39\21 - - - - - - 0\11 - - - 32\24 - - - - - 35\10 - - - 0\30 - - - - 15\33 - - - - - - 22\0 10\0 0\34 - - - - - 22\28 - - - - - - - 0\3 - - 17\22 - - - - 15\33 - - - - - 0\28 - - - - 0\36 - - - - - - - - 0\22 - - - - 0\31 - - - - - - - 0\0 However, based on the way top-down Sudoku generators work, I imagine all the generators start by choosing grid size, then pattern of black/white cells ...

then (more or less randomly) fill the white grid, then compute the sums in the black cells, and then delete sums one by one as long as unicity is preserved. I use just that method for generating Skyscraper puzzles, which was my first venture into puzzle-creating software.

I think this process is somewhat akin to what Conceptis uses for their kakuro books, at least, their puzzles and mine have lots of similar attributes.

Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Could you post one of those you consider as typical of "Absolutely Nasty Kakuro - Level 4"? However, based on the way top-down Sudoku generators work, I imagine all the generators start by choosing grid size, then pattern of black/white cells (often making it nice looking in some sense and/or with some symmetries), then (more or less randomly) fill the white grid, then compute the sums in the black cells, and then delete sums one by one as long as unicity is preserved.This example is puzzle #103: 24 rows 14 cols 0\0 0\0 30\0 45\0 35\0 37\0 6\0 21\0 24\0 0\0 35\0 17\0 42\0 28\0 0\0 16\42 - - - - - - - 0\29 - - - - 0\36 - - - - - - - - 4\19 - - - - 0\35 - - - - - 30\20 - - - - 35\15 - - 0\28 - - - - - - - 17\26 - - - - - 0\0 17\0 29\39 - - - - - - 37\21 - - - - 0\19 - - - 11\22 - - - - - 19\9 - - - 0\32 - - - - - - 45\33 - - - - - - 0\0 27\23 - - - - 16\16 - - - - - 4\0 11\0 0\29 - - - - 7\29 - - - - - 30\3 - - 0\14 - - 13\0 0\7 - - - 15\30 - - - - - 0\20 - - - 0\33 - - - - - - - 29\0 30\0 0\8 - - - 17\0 24\7 - - - 4\0 0\21 - - - 0\0 3\0 11\42 - - - - - - - 0\23 - - - 0\18 - - - - - 21\7 - - - 11\0 45\13 - - 0\4 - - 35\16 - - - - - 44\27 - - - - 0\0 29\0 41\27 - - - - - 10\23 - - - - 6\0 0\39 - - - - - - 39\21 - - - - - - 0\11 - - - 32\24 - - - - - 35\10 - - - 0\30 - - - - 15\33 - - - - - - 22\0 10\0 0\34 - - - - - 22\28 - - - - - - - 0\3 - - 17\22 - - - - 15\33 - - - - - 0\28 - - - - 0\36 - - - - - - - - 0\22 - - - - 0\31 - - - - - - - 0\0 However, based on the way top-down Sudoku generators work, I imagine all the generators start by choosing grid size, then pattern of black/white cells ...then (more or less randomly) fill the white grid, then compute the sums in the black cells, and then delete sums one by one as long as unicity is preserved. I use just that method for generating Skyscraper puzzles, which was my first venture into puzzle-creating software.I think this process is somewhat akin to what Conceptis uses for their kakuro books, at least, their puzzles and mine have lots of similar attributes.Including the fact their hards and my hards aren't very hard for a seasoned solver.I liked the idea of every solve iteration having at least one solution, so it wouldn't waste its time with totally unsolvable puzzles.The solver is coded so that if a puzzle has multiple solutions it will fail to find any of them.It'd also be nice to have the puzzles named some way, so that we can refer to them without having to post them. to what Conceptis uses for their kakuro books, at least, their puzzles and mine have lots of similar attributes.Including the fact their hards and my hards aren't very hard for a seasoned solver. I am also trying to develop Kakuro generating software, and am also familiar with Conceptis puzzles. PS: You must have also noticed, as I have, how very little information about puzzle-generation there is available in the public domain.Although maybe that's just me being bad at kakuros. I'd also love to hear a good algorithm for detecting naked triples!As most of your puzzles have obvious surface sums, it's strange that you don't use them.

]] 45[[Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||Including the fact their hards and my hards aren't very hard for a seasoned solver.

||

## Comments Kakuro Research Paper

## Ponder this - IBM Research

IBM Research - Haifa is the largest lab of IBM Research Division outside of the United States. Founded as a small scientific center in 1972, it grew into a major lab that leads the. Work with us. January 2015 Kakuro - easy version.…

## New Kakuro Generator/Site Kakuro - The New Sudoku Players' Forum.

Dec 9, 2013. I've just made live my new Kakuro site. It's got. BTW, how does your generation process work. Sometimes that fails too - I lost a whole swag of research material on Gerechte designs, ie non-standard Sudoku/Skyscraper.…

## Level Up your Brain Power with Sudoku - Lifehack

Memory and logic work side-by-side when you are playing Sudoku. We use our. Now you just need to research the possibilities of making money from it.…

## Writing a Research Paper – The Writing Center – UW–Madison

This page lists some of the stages involved in writing a library-based research paper. Although this list suggests that there is a simple, linear process to writing.…

## Color can make a large, flat kakuro puzzle look a little less.

Color can make a large, flat kakuro puzzle look a little less frightening. A flat layout on larger kakuro puzzles can be confusing. Sudoku Puzzles, Logic Puzzles.…

## The Dewey blog Mathematical or not?

Jun 20, 2006. So we assigned Sudoku and Kakuro the Dewey number 793.73 Puzzles. The Wikipedia even has an article on the Mathematics of Sudoku.…

## Mathematical puzzle - Wikipedia

Mathematical puzzles make up an integral part of recreational mathematics. They have specific. they were discussed by Martin Gardner in his "Mathematical Games" column in Scientific American. Cryptograms · Fifteen Puzzle · Kakuro · Rubik's Cube and other sequential movement. Main article Mechanical puzzle.…

## Computer Science for Fun - cs4fn Computational Thinking.

Automata Booklet Build a paper puzzle. explore finite state machines. Kakuro. A fragment of a Kakuro puzzle Logical thinking plus addition.…

## National Academy of Sciences

PNAS is one of the world's most-cited and comprehensive multidisciplinary scientific journals, publishing more than 3,200 research papers annually.…

## Math Puzzles to Engage Your Students Prodigy Math Blog

Feb 6, 2019. It might sound harsh, but it's true — only about half of students report being. Research on why math puzzles are a great idea for your classroom. Kakuro, also called “Cross Sums,” is another mathematical crossword puzzle.…