Category Archives: dissections

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.

Squares


It is trivial to divide a square into 4 squares:
Divide a square exercise illustration

Divide a square into:
a) 6 squares
b) 7 squares
c) 8 squares (2 ways)
d) 9 squares (2 ways)
e) 10 squares (2 ways)
f) 11 squares
The squares should not overlap.

A new puzzle is posted every friday. You are welcome to comment on the puzzles. Solutions are added at the bottom of a puzzle after one or more weeks.

You can check your solutions here

The ingenious pieces of Sei Shonagon


Tangram is one of the best known puzzles in the world, and went through at least two fads: one in the early nineteenth century, and once more when American puzzlist Sam Loydd published a booklet about it. The oldest known tangram dates back to about 1800.

In 1742, a little book about a Japanese seven-piece puzzle was published under the pseudonym Ganreiken. The real name of the author is unknown. The title was “Sei Shonagon Chie-no-ita”, or the ingenious pieces of Sei Shonagon. Sei Shonagon was a court lady who lived approximately 966 – 1017. There is no clear reason why Ganreiken named his 32 page booklet after her. The booklet has 42 patterns with answers, but the shapes are inaccurate. A copy of the booklet has been distributed at one of the International Puzzle Parties, but as I’m not in contact with anyone in higher puzzle circles I don’t have access to it. A year later Ganreiken published another book with more exercises. In about 1780, Takahiro Nakada wrote a manuscript entitled “Narabemono 110 (110 Patterns of an Arrangement Pattern),” and Edo Chie-kata (Ingenious Patterns in Edo) was published in 1837. Alas I was unable to find these figures on the internet.

There are surprisingly few publications in the west about this puzzle. Jerry Slocum devotes half a page of it in his book “The history of Chinese Tangram”, and Jerry Slocumn and Jack Botermans describe it in their “Zelf puzzels maken en oplossen”.

The Sei Shonagon consists of 7 pieces, like Chinese Tangram, which make up a square. Unlike Tangram, they can be fitted together to make up a square in two different ways.
sei shonagon square 1


I will leave the other square as an exercise for you.

They can also form a square with a whole in the middle:
sei shonagon square with hole in centre


The figure with the hole in the middle is one of the original puzzles.

Where the Chinese tangram has 13 convex shapes, Philip Moutou showed that Chie no-ita has 16 possible convex shapes. In geometry, a shape is called convex if any two points of the figure can be connected by a straight line which is entirely within the figure. I intend to publish about them in a subsequent post.

Presented here are 28 of the original problems.

japanese tangram blogpost 1-1 exercises

japanese tangram blogpost 1-2 exercises

japanese tangram blogpost 1-3 exercises

japanese tangram blogpost 1-4 exercises

japanese tangram blogpost 1-5 exercises

japanese tangram blogpost 1-6 exercises

japanese tangram blogpost 1-7 exercise

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.

Five triangles


1 triangle

Imagine a right triangle (formerly called a rectangled triangle). One side adjacent to the right angle is twice as long as the other. You will not find it very difficult to construct a square from 4 of these triangles.

But is it possible to construct a square from 5 of these triangles? And from 6? From 7?

These problems are derived from ‘doordenkertje’ 12 in the November 1969 issue of ‘Pythagoras’, a Dutch magazine in recreational mathematics. You will need some elementary geometry knowledge to solve this problem.

You can check your solution here

Re-assemble please


1) A**
Dissection A 2013-11-09 exercise
I think that in several puzzle magazines I found puzzles in which is figured has been divided into several parts, ands where it’s up to the reader to re-assemble the pieces.

The puzzle to the left is one example. You can see the figure, and you can see the pieces, and it’s up to you to put them together again.

(oh, and this an original puzzle, not copied from any source)

2) Tangrams
TangramTangrams of course deserve it’s own blog post. It is no doubt one of the most extensively published puzzles. One of the books I used to have (somehow got lost) had over a thousand figures. The square is dvided into several pieces, and should be re-assambled in any of the shapes published in the accompanying puzzle books.
Among puzzlers it is well known that American puzzlemaster Sam Loyd gave this puzzle the name Tangram. Its history has been researched in detail by acknowledged puzzle collector and puzzle master Jerry Slocum

3) Leiden
Leiden puzzle cutTangrams are not unique. There is a similar chinese puzzle in the Volkenkunde Museum in Leiden, composed of 14 pieces. The booklet has been preserved, but it’s 14 pieces are missing. On the left you see one illustration from the booklet that can be assembled with these pieces. I would like to thank the Volkenkunde Museum in Leiden for sending me a scan of this booklet.

4) Japan
This type of puzzle not only florished in China, but also in Japan. In 1742, a little book about a Japanese seven-piece puzzle was published under the pseudonym Ganreiken. The real name of the author is unknown. The title was “Sei Shonagon Chie-no-ita”, or the ingenious pieces of Sei Shonagon. Sei Shonagon was a court lady who lived approximately 966 -1017.
I intend to do a separate post on this puzzle.

You can check your solution to puzzle nr 1 here

A new puzzle is published every friday. The solution is generally published one week later. I welcome your reactions on these puzzles: are they too easy, too difficult, are there any multiple solutions? How long did you need to solve it?

Dissections – the Greek cross (2)


A few weeks ago I posted some . Unfortunately I overlooked some of the puzzles created by Sam Loyd, so here is part 2. Sam Loyd must have been really fascinated by this shape, judging from the number of times he wrote about it.

1) Red Cross Volunteers
Red cross volunteers
Here is a pretty little crutting puzzle, which is said to have originated in the mind of a red cross lassie while serving in Uncle Sam’s Ambulance Corps. It is safe to say that the bright witted little volunteer must have been a lineal descendent of Betsy Ross, who, it will be remembered designed the five-pointed star with one deft clip of her scissors. In the present instance it was necessary to practice strict economy in the manufacture of the red crosses to decorate the arms of the nurses, for the reason that the supply of red flanel was running very short in camp, so the problem presented is as follows: take a square pices of paper and without any waste cut it into five pieces which will fit together so as to make two Greek crosses of the same size.
This problem appeared on pages 199 of Sam Loyds cyclopedia of puzzles.

You can find the solution here

2) Divide the greek cross into three pieces
Sam Loyd Easter 1903
To illustrate the principle of working a puzzle backward, according to the axiom that a good rule should work both ways, we introduce a seasonable problem wherein the object is to discover how to divide a cross into three pieces which can be fitted together so as to form a rectangle which is twice as long as it is wide.
This, of course, is merely reversing the proposition of converting a rectangle into a greek cross, but, in that it presents the angles which must be fitted together, it is not so difficult as the other proposition.
This problem appeared on page 46 of Sam Loyds Cyclopedia of puzzles.

You can find the solution here

3) A swiss puzzle
A Swiss puzzle exercise
Here is a very pretty trick performed by Miss Carré Schwitzer, which rivals Betsy Ross’ feat of producing a five pointed star with one clip of the scissors. When admiral Schwitzer asked his daughter to suggest an ensign for the Swiss navy, Carré seized an odd shaped remnant of red wall paper and skillfully divided it in two pieces which would fit together so as to form the Swiss flag with the white cross, as shown in her left hand.
When she was told of Betsy Ross’ feat she said she could go her one better. She took a Swiss flag, as here shown, and cut it into two pieces which would fit together and form a perfect square.
Swiss flag exercise 2
Of course if you can make a Swiss flag from a square, it is just as easy to reverse the operation – cut a square in two pieces which will form a flag.

4) The storm signal
Carré performed other feats with the Swiss flag which we will take occasion to mention. When she had charge of the signal station on Mt. Pilatus and whished to signal the fleet that a storm was rolling down the mountain, she took a square piece of bunting and cut it into two pices which would fit together and form the following flag.
Swiss flag exercise 3
In the Swiss language this tells of an approaching storm. Literally translated it says: “There will be a hot time in the old town tonight.”
Just to see how clever Miss Schwitzer was, try to cut the signal flag in two pieces which will form a perfect square.

5) Miss Schwitzer cont’d
Miss Schwitzer always acted on the square and was much respected on that account. She taught her Sunday School class how to cut three little squares into the fewest possible number of pieces so as to form one big square, and also the way to cut the three squares so as to form a Swiss cross. Try both of these puzzles.
Swiss flag exercise 4

6) Wilhelm Tell
William Tell asked her how to make a Maltese cross and she replied “Pull its tail”. She founded the order of the red cross.
Swiss flag exercise 5
There are two very beautiful puzzles connected with this cross, which are worth knowing: Cut the cross in two pieces which will form a rectangle, or cut it in three pieces which will make a perfect square.
We shall take early occasion to mention some of the marvelous feats performed by Carré Schwitzer in cutting Swiss cheeses, and juggling with pans of milk at her Swiss milk factory, near the chalk hills of Luzerne.

Problems 3-6 can be found on page 14 of Loyds cyclopedia of puzzles.

You can find the solutions for:
nr 3,
nr 4
nr 5
nr 6

7) The greek cross
There are also a number of puzzles on page 58, but I think they are largely overlappping with the puzzles above.

Magic snake


The magic snake is a plastic puzzle manufactured by Shuo Yi toys factory, Shang Hua town, China. It is constructed of a series of half cubes, cut diagonally, and connected with what loooks like a string. I don’t know the price, it’s a present given by “Black Pete”.

The packaging looks cheap, and the back carries the images of 9 3D figures which can be constructed with it.

Here are some more figures which you may wish to create:
magic snake flower mini 20131201_203705

magic snake stairs mini20131201_190442

magic snake knot white mini 20131201_130846

magic snake knot green mini 20131201_130547

magic snake cylinder mini 20131201_123846

magic snake cobra 20131201_121013

magic snake rectangle mini 20131201_092023

figuren en kerst 001

figuren en kerst 009

figuren en kerst 011

figuren en kerst 012

figuren en kerst 006

DSCN1952

Dissections – the Greek cross


The Greek cross consists of 5 squares joined in the shape of a cross.

1) Greek cross – 4 equal parts*
Greek cross 4 equal parts exercise
The figure above shows a strangely formed meadow between a brook and mountains. There are 4 wells in the area. The farmer died and stipulated in his will that his land would be distrubuted equally among his 4 sons; all 4 lots would have the same area and shape and contain exactly 1 well.

How was the land divided among the 4 sons?

2) The hindu problem
Dudeney Greek cross dissection problem
The greek cross as shown in the illustration to the left, is composed of 5 equal sized squares. Cut the cross into five pieces to form a square. There are 2 solutions. According to British puzzle master Henry Dudeney, the problem is over 3000 years old.

3) How many straight cuts?
Henry Dudeney next comes up with the problem:
How many cuts do you need to divide the Greek cross into 4 pieces, so that with these pieces you can form a square?

4) The Red CRoss Lassie
American puzzle master Sam Loyd recounts the following problem:
Red Cross Lassie
In the whole realm of puzzledom, and geometry included, there is nothing so fascinating and eminanetly scientific as the series of problems pertaining to the form of the Greek cross and its peculiar relations to the square, parallelograms and other symmmetrical shapes.
As differing from the well known mathematical problem of converting the cross into a square by the fewest possible number of cuts, attention is called to the following pretty feat of chaninging one cross into two.
It appears that one of our wounded boys in blue who was returning home after being nursed back to life by a faithful Red Cross lassie, begged the red cross from her arm as a keepsake; but she, in true sweetheart style, took her scissors and by a few deft clips, cut the red cross into several pieces, which could be fitted together perfectly so as to make two crosses of similar vsize. It is a simple but beautiful trick, and the satisfaction of guessing it will be as great as if you should win a prize.

You can check your solution here for no 1, here for no 2 and here for no 3, and here for no 4

A new puzzle is published every friday. The solution is generally published one week later. I welcome your reactions on these puzzles: are they too easy, too difficult, are there any multiple solutions? How long did you need to solve it?

Parks


A Park puzzle has only two rules:
1) Every row, column and park has exactly 1 tree;
2) Trees are not adjacent horizontally, vertically or diagonally.

1) The stats*
Parks - stats - exercise

2) parks 7×7*
Parks 7x7 2013-09-10 exercise

You can check your solution here and
here.

Did you know?
My current customer has the nice habit of allowing its employees a certain amount of freedom. It aint as much as Google’s former 20% free time, but it does offer facilities such as posting reflective sayings. One I came across is:

If you think adventure is dangerous, try routine. It’s lethal. (Paulo Coelho)

This may be not be literally true of the body, but I believe it’s certainly true of the mind. Brains which do not regularly encounter new challenges, develop less well when young and detoriate faster when old.

One thing I consciously try to do is presenting new puzzles. And not just new puzzles, but also present a new type of puzzle. This means your brain has to start afresh with a new problem. You have to figure out new ways to tackle this challenge.
By presenting several puzzles of the same new type your brain has a chance not only to discover HOW to solve them, but also to let these ways reach the conscious state. You realize what the new tricks are with which you can solve these problems. And that is an important element of acquiring new skills (and I suspect for your brain an important part of creating new neural connections)