Dissections – the Greek cross

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

1) Greek cross – 4 equal parts^*

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

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:

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^*

2) parks 7×7^*

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)

Review metal puzzles from TTIE and Eureka

This is one of three reviews to be published this summer while i’m away on holiday,

This post is about metal puzzles that I received for my birthday and fathersday. My thanks go to the family members who donated them.

The metal puzzles from T.T.I.E, PO Box 62 2420 AB The Netherlands are a series of sturdy metal puzzles. They come in grey boxes, which are mostly of a standard size.

Many of the smaller ones look like standard problems, consisting of 1 twist. I was not able to find their website, zo it is probably not a very big firm.

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Two of the puzzles I received are more original, they come from Eureka! 3D puzzles. The one with three rings is nice, I havent seen it before, though all the elements are very standard.

The puzzle which I christianed “Double E” is a nice one. It took it with me to the office, where my puzzle friends quickly solved it. Then I twisted them into each other again, and somehow we have been unable to separate them again.

You can find the website of the supplier at http://www.eureka-puzzle.eu/eureka, though they only sell to retailers, and dont seem to sell to individuals.

Review crystal jigsaw puzzles

This is one of three reviews to be published this summer while I’m away on holiday,

This post is about plastic 3D jigsaw puzzles that I received for my birthday and fathersday. My thanks of course go to the family members who donated them.

Now I must confess that I dont like jigsaws puzzles. One reasons is they are way too common for my taste. Another reason is that they do not tax my brain enough: it needs diligent work, but not hard work.
But when it comes to 3D puzzles, the borderline becomes fuzzy. Ravensburg has published 3D jigsaw puzzles for I estimate over a decade. All pieces look like ordinary pieces, except they are thicker, so you can build walls and roofs with them.

On the other end of the 3d spectrum are the Japanese kumiki puzles, often beautifully made of wood, and representing several types of buildings, animals, fruit and other objects.

Somewhere in between are the plastic 3D jigsaw puzzles. I discovered them on the web, as produced by Kimzel Gmbh in Germany. They have a series of about 40 models. I ordered mine through Moenen and Mariken. This shop is in Dutch, and I can recommend their service, which was excellent.
If you live in the USA, you can order them from Amazon, where they are marketed by BePuzzled.

The number of pieces varies greatly. I have an apple of 13 pices, several of 46 pieces, and I have seen some of 90-100 pieces. Despite their name, they are not really crystal, but a sturdy plastic that looks like it. The copyright belongs to Beverley Enterprises Inc. & Jeruel Ind Co Ltd. The latter is a China based Toys and Puzzle producer, and the puzzles are produced in China. The pieces fit together really well. I guess the plastic does make them affordable, prices range from 3-20 euros.

Review Hanayama puzzles

This is one of three reviews to be published this summer while i’m away on holiday,

This post is about metal puzzles that I received for my birthday and fathersday. My thanks of course go to the family members who donated them.

The Hanayama series is a series of beautiful iron cast puzzles published by hanayame toys in Japan.

There are 2 kinds of packaging around, one is a beautiful shiny red/black cardboard box, the other a dull grey-green? cardboard box, which I dont have myself but did see on ads in the USA.

The puzzles themselves are very solid, and have varying degrees of difficulty. The manufacturer has them labeled with a number of stars, more stars meaning more difficult. Many of the puzzles have been designed by well established names in the puzzle world such as Oskar van Deventer and Nob Yoshigahara.

New puzzles seem to be published regularly, and can be mail ordered at several places:

• https://www.nextag.com/hanayama-cast-puzzle/products-html#!
• http://www.zoompuzzles.com/hanayama_cast_puzzles.html
• http://www.brilliantpuzzles.com/Hanayama_Cast_Puzzles.html

They have varying degrees of difficulty, 1-5, and come without a solution, though you may try the generally know video sites if you are completely stuck. I now have one of the rings, the cast duet and the cast quartet, and probably one or more others, and I’m very satisfied with them. There must be somewhere between 50 and a 100 of them by now,

Soma cube – part 2

Some time ago I presented some new soma cube puzzles. If you dont know what a soma cube is, have a look here.

Here are 8 new figures:
1) wall

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2) stairs 1

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3) airplane

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4) stairs 2

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5) castle wall 1

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6) gate

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7) castle tower 2

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8) castle tower 3

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If you solved it, we have the solution to
wall,
stairs 1,
airplane,
stairs 2,
castle wall 1,
castle gate,
castle tower 2,
castle tower 3,

Soma cube

Though this blog mainly concentrates on logical puzzles, this post is about the Soma Cube, invented by Danish scientist Piet Hein in 1933 during a lecture on quantum physics. The name SOMA may be related to the name of an array.

It is a solid dissection puzzle, where a 3x3x3 cube is divided into 7 pieces:

You can easily create your own set with a saw and some wood glue.

The Soma cube has been discussed in detail by Martin Gardner and John Horton Conway, and the book Winning Ways for your Mathematical Plays contains a detailed analysis of the Soma cube problem. There are 240 distinct solutions of the Soma cube puzzle, excluding rotations and reflections.

Piet Hein also published or authorized a booklet with puzzles. I found a copy here. However, I found 2 figures with a number of blocks less than 27, so I have discarded them and added two of the problems listed below in this file.

Here are some problems I did not find elsewhere on the web:
1)

2)

3)

4)

5)

6)
(Thanks go to fellow consultant Harrie Jans for this one!)
7)

8)

Many people noticed that the pieces used are not all tetracubes, and the tricube is a strange duck in the pond. In response several people have suggested something dubbed Soma+, but that is a subject for a different post in this blog.

There is an awful lot of literature on the web. Here are some links:
* Thorleif Bundgaard collected a very nice and very extensive collection of figures which can be made with the soma cube pieces.
* Chapter 24: Pursuing Puzzles Purposefully from the book “Winning Ways II “
* Article on english wikipedia on soma cube
* Article on englsih wikipedia on tetrominoes
* List of figures
* All 240 solutions to the cube
* Instructions for making a soma cube

If you solved it, we have the solution to nr 1, nr 2, nr 3, nr 4, nr 5, nr 6, nr 7, and nr 8