It is trivial to divide a square into 4 squares:
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
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.
I will leave the other square as an exercise for you.
They can also form a square with a whole in the middle:
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.
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.
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.
puzzle 2*
This time only some empty positions have been given as clues.
puzzle 3**
Again only some empty positions have been given as clues.
You can check your solutions here
A new puzzle is published every Friday.
I had to tile the floor of a room which was to 2 meters long and 2 meters wide. I had boards of 20 cm wide and either 1.60 or 1.80 meter long. How many boards do I have to saw so that I can cover the entire floor?
You can check your solutions here
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
Puzzle 2
Puzzle 3
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.
“Our prisoner nearly dug his way out, oh mighty Sultan,” the chief keeper of the prison told the Sultan, “because the rock our prison cells are made of is so soft.”
“Which prisoner are you talking about?” the Sultan asked.
“The one who laid eyes on the eyes of your favorite wife, Oh mighty One,” the chief keeper of the prison replied.
The Sultan moved uneasily when hearing these words, as one of his other wives was in the room.
“What do you suggest?” the Sultan asked.
“The prisoner had started to dig out a tunnel,” he replied. “We have a prison with 9×9 grid of prison cells. If we move him to another cell every day, he will not be able to dig a tunnel.”
“What will you do when he is in the 81th cell?” the Sultan asked.
“Again move him to a new cell, which will be the one in which he is now,” the chief prison keeper replied.
“OK. But don’t spend to much time on him,” the Sultan said. “Always move him just to a cell that is horizontally or vertically adjacent.”
Can the keeper of the prison move the prisoner in such a way that the prisoner is moved to an adjacent cell and visits every cell exactly once, and is moved back to his current cell on the 82nd day?
You can check your solutions here
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
In Mathematics, an isosceles trapezium is a quadrilateral one pair of opposite sides are parallel and the base angles are equal in measure. Alternative definitions are a quadrilateral with an axis of symmetry bisecting one pair of opposite sides, or a trapezoid with diagonals of equal length.
How many isosceles trapeziums do you count in this figure?
Just for the sake of clarity, three triangles in one row would make an isosceles trapezium, as the red one in this example:
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.
1) A**
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
Tangrams 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
Tangrams 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?
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.
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.
justpuzzles 