Monthly Archives: January 2013

Complete the alphabet (2)

1) Complete the alphabet*


In which row does the letter Z go?

If you solved it, we have the solution so you can check yours

One of the nice things of wordpress is its detailed visitor stats.
This blog had 6900 views in 2012.

The visitors have come from (in from most to fewer, only countries > 5 views represented:

United States India United Kingdom Netherlands Canada Australia
Ireland, Philippines Singapore Belgium Turkey Pakistan Germany Romania
Saudi Arabia France Spain Brazil Jordan Korea, Malaysia Hong Kong Greece
Poland Denmark New Zealand Italy Indonesia United Arab Emirates Norway
South Africa Sweden Taiwan Switzerland Mexico Algeria Israel Austria
Lebanon Finland Portugal Qatar Iceland Iraq Hungary Kuwait Jamaica
Ukraine Nigeria Russian Federation Egypt Serbia Bangladesh Japan
Thailand Belize Slovakia Viet Nam Nepal Argentina Latvia Kenya Estonia Armenia

There were 38 new posts, brining the total up to 52. 127 new pictures were uploaded.
The busiest day of the year was December 17th with 97 views.

The most popular posts date back to 2011, all types of river crossing puzzles.
Oh, and the most poopular page was the page with the solutions.

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:
Somacube 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:
soma cube figure c01
soma cube figure c02
soma cube figure c03
soma cube figure c04
soma cube figure c05
soma cube figure c06 (Thanks go to fellow consultant Harrie Jans for this one!)
soma cube figure c07
soma cube figure c08

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

1 lightbulb and 100 prisoners

1 lightbulb and 100 prisoners illustration
1) 1 light-bulb and 100 prisoners***
Once upon a time there were 100 prisoners, all confined in solitary cells. At the center of the prison is a strip of grass with a small cottage with a light-bulb.

One day the evil Nazi commander of the prison camp calls the prisoners together. He tells them:
“Once a day a random prisoner will be allowed to breath fresh air on this strip of grass in the center of our beloved prison. From this the lucky prisoner of the day has access to a small cottage with a light-bulb, which he can switch on or off.
When one of you thinks you have all been here at least once, and states so correctly, you will all receive free library access. If the prisoner is incorrect, you will all end up before the fire squadron.
You now have 1 evening to discuss a strategy, and then its: back to your solitary cells, and no longer any contact.”

What is a good strategy for the prisoners to decide upon?

This puzzle was first presented to me by Jon Koeter, whom I mentioned before. My fellow consultant Harrie Jans surprised me this week by solving it in 1 minute.

You can check your solution at no 210

Did you know?
Showing a brain image besides text makes people believe the text