Category Archives: Mathematics

TooT


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

Horizontal
1) 16, 17, 18
3) 20, 26, 36
4) 142, 139, 145
8) 6819, 20002, 30134
11) 18, 20, 22
12) 11, 24, 36
Vertical
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

Horizontal
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
Vertical
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

Horizontal
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
Vertical
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.

Matchstick – triangles


Surface***/*****
These 6 matches enclose an area with size 2 (2 standard triangles).
Rearrange them so that:
a) they enclose an area of exactly 4 triangles
b) they enclose an area of exactly 6 triangles

matchstick-triangles-2-2016-12-14-nr-1-exercise

You can check your solutions 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.

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**/*****
calcudoku-4x4-2017-01-10-nr-1-exercise

You can check your solution here

2) 5×5**/*****
calcudoku-5x5-2017-01-12-nr-1-exercise

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: :
calcudoku_justpuzzles

Techniques for solving them:
* http://www.conceptispuzzles.com/index.aspx?uri=puzzle/calcudoku/techniques
*

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:
binairy-puzzle-6x6

puzzle 1: 6×6:***/*****
binairy-6x6-2016-11-30-nr-1-exercise

puzzle 2: 7×7:***/*****
binairy-7x7-2016-11-30-nr-1-exercise

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.

Ages


Ages**/*****

coupleAges**/*****
A man is 25 years old and his wife 23. He noticed that the sum of their ages (25+23=48) is exactly 4 times the sum of the digits of their ages. (2+5+2+3=12).

When will the sum of their ages be exactly 8 times the sum of the digits of their ages? And when will it be 9 times the sum of the digits?

You can check your solutions 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.

Find a 4 digit number


Number**/*****
Find a four digit number abcd such that
– abcd is a prime number,
– a+b+c+d = 10,
– the sum of the digits of ab*cd equals 7.

You can check your solutions 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.

On the first day of Christmas…


1) On the first day of Christmas**/*****
On the first day of Christmas, my true love brought to me:
On the first day of Christmas
My true love gave to me
A partridge in a pear tree

On the second day of Christmas
My true love gave to me
Two turtle doves
And a partridge in a pear tree

Thus go the first two couplets of a traditional Christmas song. Question is:
Haw many things did my true love give me over these 12 days? (counting the partridge in the pear tree as one item)

You can check your solutions here

2) On the second day of Christmas**/*****
Yeah, in puzzle 1 above you had the classical song. But in puzzle land, everything is different.
In puzzle land, on the second day of Christmas my true love brought me this puzzle:

“This puzzle consists of @ letters”

With what number (spelled out, of course) should @ be replaced to be true?

You can check your solutions here

3) On the third day of Christmas**/*****
On the third day of Christmas, my true love brought to me this puzzle:

“This puzzle consists of @ vowels and # consonants”

Again, by which numbers, spelled out, should @ and # be replaced to yield a true sentence? Please note that “y” is counted as a vowel.

You can check your solutions 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 three stars.

The anchor puzzles


Starting in 1890, the German firm Richter produced a series of Tangram puzzles which were widely distributed during the First World War, or The Great War as it was then called, as a pastime for the troops in the trenches. With the pieces consisting of stone, they could survive in the horrible environment. They were used by both German and British troops.
The puzzles came together with sheets with exercises, which have been compiled by Jerry Slocum, one of the worlds greatest puzzle collectors. He published the exercises in a book, which you can order here. The firm stated that some of the problems have been contributed by the troops.
The anchor factories are now owned by Goki.

I recently purchased a series of anchor stone puzzles at internet-toys.com (Another supplier is http://www.padilly.com/brainteasers.html). Their delivery was speedy and accurate, and they have low prices. The puzzles arrived within a few days, though of course I can not vouch for delivery times in the rest of the world.
The puzzles are still made of stone, and below you find pictures of the once I obtained. Currently they do not offer the full range. The ones they do offer are in bright green, yellow, blue and red. The back of the cardboard boxes do mention Anker Steinbaukasten GmbH. There are no names of the individual cardboard boxes. Some of the boxes carry a number of puzzles on the inside of the box, some don’t. None had a solution, and the drawings on the cover do not match the inside arrangement of the pieces. This, the boxes state, is on purpose: no clue is given away. You did want to puzzle, did you?

There are 3 historical puzzles, which in “Puzzles old and new” by Jack Boterman and Jerry Slocums are called Zornbrecher, Wunderei / Ei des Columbus (I don’t see much difference between these two in their book) Herzratsel and Kreisratsel. These are the ones that come with the 10 exercises on the inside of the box.

The big surprise for me are the other puzzles: The do not seem to match any of the traditional Anker puzzles. At internet toys they are labelled maan, dennenboom, ster en kruis in Dutch, which translates into English as moon, pine, star, and cross.

Expect some exercises in the future with these new puzzles, though the usage of non rectangular shapes may cause some troubles in this endeavor. For the moment, here are the puzzles:

dsc_3676-anker-kreisratsel dsc_3678-anker-ei-columbus dsc_3682-anker-zornbrecher
dsc_3683-anker-herzratsel dsc_3675-anker-pine dsc_3679-anker-cross
dsc_3680-anker-moon dsc_3681-anker-star

New puzzles are published at least twice a month on Fridays. 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 three stars.

Japanese tangram


A few weeks ago I wrote about a Japanese Tangram from 1742, pre-dating the well known Chinese Tangram, and gave some classical figures with the 7 pieces. This week I’d like to present some figures wit the theme: In and around the water.

Japanese tangram post 2 image 1 exercise

Japanese tangram post 2 image 2 exercise

Japanese tangram post 2 image 3 exercise

Again I’d like to thank my wife Jos and our daughter Margreet for coming up with these figures.

You can check your solutions here

A new puzzle is published every Friday. Solutions are published after one or more weeks. You are welcome to discuss the puzzles, their difficulty level, originality and much more.