Category Archives: Pencil and Paper puzzles


Sanders, the most innovative puzzle magazine publisher in my native Netherlands, recently published a new variation of Nonogram, also referred to as Hanjies, grid puzzles, picross or, in Dutch, Japanese Puzzles (Japanse puzzels).

It uses triangular grids instead of the customary square grids, which adds a nice touch to this puzzle type. This puzzle type is sometimes called Triddlers, and comes in two types:
(a) the triangles are the half of a square.
(b) These triangles are equilateral triangles, with 60 degrees in every corner.
The puzzles in this publication arte of the latter type, which I much prefer. A nice feature is the inclusion of a small puzzle alongside a big one on every page. Well recommended!
You may wish to try to obtain one through their webshop, I just discovered they now ship internationally.

(Apologies for not including a sample puzzle this post, I havent yet discovered good tools for making good triangular or hexagonal grids. Tips are appreciated, plz add them in the remarks section)


In this post I’d like to introduce TooTs, a mix between crossword puzzles and numbers. The grid looks just like a crossword puzzle, but instead of words the grid has to be filled with numbers. Vertical numbers must be read top-down. Thus if the digits 3, 9 and 5 are listed from the top down, the number would be 395.

Every clue consists of three numbers. Two of them have to be added together to get the number to be filled into the grid.
Example: the clue is 7, 8 and 13. Then the solution is either 7+8=15, 7+13=20 or 8+13=21. The name TooT is shorthand for Two out of Three.

Here is a 5×5 exercise:
Toot 5x5 2015-04-24 exercise

1) 16, 17, 18
3) 20, 26, 36
4) 142, 139, 145
8) 6819, 20002, 30134
11) 18, 20, 22
12) 11, 24, 36
2) 17, 19, 23
3) 18, 36, 47
5) 400, 406, 418
6) 18, 106, 256
7) 15, 25, 190
9) 1, 51, 61
10) 11, 12, 13

A 7×7 exercise:
Toot 7x7 2015-04-24 exercise

1) 16891 18930
6) 382, 23, 67
8) 25, 8, 17
10) 32, 14, 17
11) 2913476, 173823, 1876543
12) 61, 23, 38
13) 45, 11, 34
14) 865, 249, 444
16) 13947, 1171, 5419
2) 53, 26, 27
3) 8843269, 332160, 345612
4) 22, 3, 5
5) 12263, 5321, 6942
7) 62652, 23487, 39165
9) 591, 109, 482
10) 374, 25, 98
14) 83, 16, 26
15) 54, 17, 27

You can check your solution here and here

A 9×9 puzzle:
Toots 9x9 2015-05-15 nr 1

1. 108, 132, 146
4. 2, 166, 660
6. 2497, 9892, 12837
9. 0, 7, 24
11. 212, 669, 774
12. 4, 19, 30
13. 18, 27, 27
15. 14, 33, 40
16. 242, 977, 2236
17. 596, 903, 2770
18. 25, 31, 52
20. 4, 11, 22
21. 7, 9, 35
22. 126, 343, 422
24. 3, 10, 13
26. 2918, 74181, 82214
28. 292, 320, 398
29. 66, 191, 228
1. 38, 96, 224
2. 4, 41, 77
3. 239, 1644, 4146
4. 19, 29, 35
5. 3, 7, 227
7. 20, 36, 38
8. 1, 14, 17
10. 12591, 13966, 31881
12. 706, 10961, 36955
14. 186, 210, 367
15. 102, 153, 279
19. 2287, 3330, 3945
21. 112, 239, 304
22. 19, 26, 45
23. 6, 23, 87
25. 74, 299, 315
26. 33, 49, 52
27. 12, 12, 12

You can check your solution here and here

In a subsequent post, probably next month, I hope to publish some variations.

Calcudocu / K-doku / Calcdoku

Calcdoku problems, also called K-doku or Calcudoku were invented in 2004 by Japanese math teacher Tetsuya Miyamoto, who intended the puzzles to be an instruction-free method of training the brain. He used the Japanese name KenKen, which could be translated as ‘Cleverness’. In his classes, he sets aside about 90 minutes each week for solving puzzles. He believe that when students are motivated, they learn better, and he lets them do so at their own pace.
Other names used for this type of puzzle are Kendoku and Kashikoku naru Puzzle. The names KenKen and Kenduko are trademarked. Books are in Japan published by Gakken Co. In the USA the New York Times started publishing them in 2008. In my native Netherlands they appear regularly in both puzzle magazines and general magazines.

A calcudoku puzzle consists of a latin square – a latin square can have any size. If its size 4, the numbers 1 to 4 should appear exactly once in every rown and column exactky once. Similarly, if its size 5, the numbers 1-5 should appears exactly once in every row and column.
The square is subdivided into smaller areas, and the sum, product, difference or division result is given in the top left corner.

Here are two example puzzles.
1) 4×4**/*****

You can check your solution here

2) 5×5**/*****

You can check your solution here

3) 6×6****/*****
is an example puzzle, kindly offered by Jacques Min, who runs a website specialized in Calcudoku puzzles: :

Techniques for solving them:

You can check your solution here

New puzzles are published at least twice a month on Friday. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.

Takuzu / Binairo

Takuzu (often called Binairy/Binairo or occasionally Tic-Tac-Toe) puzzles have been around for several years. In my native Netherlands they have been published by both Sanders puzzles and by Denksport, and also in daily newspaper Algemeen Dagblad.
In France, they have been published under the name Takuzu in le Figaro, at least in 2011.

The puzzle consists of a rectangle or square with an even number of rows and columns. This is partly filled with 0’s and 1’s. It should be completed by the solver with 0’s and 1’s in such a way that:
a} There are never more than two consecutive 0’s or 1’s in any row or column;
b) There are an equal number of 0’s and 1’s in every row and column;
c) All rows and columns are different;
This last condition seems to be rarely used in the commercial publications. Sizes are usually 10×10, 12×12 or 14×14, though 6×6 and 8×8 are often offered as introduction puzzles.

Example 1:

puzzle 1: 6×6:***/*****

puzzle 2: 7×7:***/*****

You can check your solutions here and here

New puzzles are published at least twice a month on Friday. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.

Chaos checks

In september last year, I wrote about ‘Vinken’ or ‘Checks’, a Sanders puzzles publication. My main comment was that it was a nice puzzle variation, but that the puzzles were slightly too easy. Sanders puzzels corrected this in later issues.

I did come up wit a slight variation, though the puzzle I designed didn’t make the puzzle difficult enough for my tast. Anyway, I’d like to present this variation to the world.

The rules are simple:
– every row and column, and every 9 sized area, contains 3 checks.
– the checkmarks are never adjacent horizontally or vertically. They may be adjacent diagonally.
– some checkmarks have been pre-filled, as well as some empty squares.

Here are three examples.
puzzle 1*
As you can see some checks and some empty positions have been given. You hve to derive the position of the remaining checks.
Vinkies-chaos 9x9 nr1 exercise

puzzle 2*
This time only some empty positions have been given as clues.
Vinkies-chaos 9x9 nr2 exercise

puzzle 3**
Again only some empty positions have been given as clues.
Vinkies-chaos 9x9 nr3 exercise

You can check your solutions here

A new puzzle is published every Friday.

Vinken – Checks

One of the leading puzzle publishers in the Netherlands, Sander Puzzels, recently came up with “Heggies en Vinken”. It introduces two new puzzles types, “Heggies” (which I suggest to translate as Hedges) and “Vinken” (translated in this post as Checks). Both are invented by Ron Mentink.

Though Heggies is probably the more interesting, in this post I would like to concentrate on Vinken/Checks. I hope to review Heggies / Hedges in a later post.

In Checks puzzles, a 9×9 grid is given. Every row and every column contains exectly 3 Checks, which are never horizontally or diagonally adjacent. Some of the empty locations have been marked with an X, and it is your task to deduce where the Checks are located.

Puzzle 1
Vinken 2015-8-23 exercise nr 1

Puzzle 2
Vinken 2015-08-25 nr 2 exercise

Puzzle 3
Vinken 2015-08-23 nr2 exercise

Personally I found it a reasonably nice puzzle. One drawback is that all clues are horizontal or vertical, with no combinations of the two clues. That is, I have been unable to come up with any situation which can only be solved with a combination of a horizontal and a vertical clue, and not with just one of them. I think there is room for improvement on this puzzle design.

If you like this puzzle or not is probably a matter of taste. If you like it, you may want to mail order some (no, I dont get a commision). At the moment I write this there are 2 issues available in their webshop. Though the website is in Dutch, and the rules are in Dutch, and the magazine is in Dutch, the ordering process should be fairly straight forward, and settng the language in Chrome should be sufficient. The puzzles can be made without any knowledge of Dutch.

You can check your solution of puzzle 1 here

You can check your solution of puzzle 2 here

You can check your solution of puzzle 3 here

Update November 28, 2015:
In issue 4, the publisher increased the difficulty level and I like this 🙂
Much better now.

123 rectangles

Complete the diagram below according to the following rules:
* Every 3×1 rectangle has exactly one 1, one 2 and one 3.
* Identical numbers are never adjacent.
* Every row has three 1,’s three 2’s and three 3’s.
As for the second rule, identical numbers may not be adjacent horizontally or vertically, they may be adjacent diagonally.

Not adjacent abc exercise

I found this type of puzzle in the children section of “PUZZEL”, an extra end-of-year addendum to the Reformatorisch dagblad newspaper, and found it good enough for this blog.

You can check your solution at here

Please try to solve the puzzles on your own: your self confidence will grow. You are welcome to remark on the puzzles, and I love it when you comment variations, state wether they are too easy or too difficult, or simply your solution times. Please do not state the soultions – it spoils the fun for others. I usually make the solution available after one or two weeks through a link, which allows readers to check the solution without the temptation to scroll down a few lines before having a go at it themselves.

Slitherlink puzzle

Slitherlinks are one of 20+ puzzle types invented by or first published by the Japanese puzzle firm Nikoli.

The rules are simple: draw one line through the grid, in such a way that
a) it forms one closed loop, and
b) in each cell the number of borders matches the number in the cell, and
c) the loop may not touch itself, not even its corners.

Slitherlink example02



So try your hand at a small puzzle:
1) 5×5

Slitherlink 5x5 handmade exercise




There are good guides with solving techniques at:
* nikoli
* English wikipedia
* Conceptis puzzles

2) 8×8
Slitherlink handmade 8x8 exercise 2013-01-31




3) 9×9
Slitherlink handmade 9x9 2013-02-06 exercise




4) 10×10
Slitherlink loopy grid 10x10 exercise easy




5) 5×5 honeycomb
We need not restrict ourselves to squares. Here is one example with a honeycomb.
Loopy honeycomb 5x5 exercise easy

The last one is a screenshot from the Loopy program, which you can freely download from Simon Tatham sportabel puzzle collection.


This puzzle type has nothing to do with the game “letter boggle”.

As usual, the rules are simple:
– fill in the entire alphabet, using every letter exactly once;
– consecutive letters are adjacent horizontally, vertically or diagonally;
– a letter in the border means that the letter appears in the indicated diagonal, row or column;

In the following puzzle, some letters are given to help you start:
1) Letterboggle*
Letter boggle 2013-12-30 nr 1 - exercise

I found this type of puzzle in “PUZZEL”, a year-end addendum to the newspaper reformatorisch dagblad. It had 2 puzzles of this type, copyrighted M. Balmaekers, though Mr. Balmaekers used a 5×5 square and dismissed the letter Q. I intend to have more puzzles like this in one of the upcoming e-books.

I would like to encourage you to solve this puzzle on your own. It will increase your self confidence, while looking up the answer will lower your self esteenm.>When you have solved this puzzle, you can check your solution here

You are welcome to remark on the puzzles, and I love it when you comment variations, state if they are too easy or too difficult, or simply your solution times. Please do not state the solutions – it spoils the fun for others. I usually make the solution available after one or two weeks through a link.