Tag Archives: math

167. Kryptos – The Unsolvable Sculpture

Kryptos is a sculpture outside of the CIA headquarters in Virginia, America. It consists of four copper panels each of which is covered in code. Letters which spell out nonsense, until you figure out the encryption. Each of the four panels is encrypted in a different way. Since its installation in 1990 three of the four panels have been decoded. Part remains unsolved after these 20 years despite the efforts put in by the employees of the CIA and thousands of cryptanalysts. This fourth and final panel of Kryptos is now one of the most famous unsolved codes in the world.

The sculpture was a $250,000 piece by Jim Sanborn. Around the CIA site he placed many other, smaller but similar copper panels with messages in morse code engraved in their surfaces; for Kryptos another level was required. A message was created, split into four panels then each encoded with the help of the chief of the CIA Cryptographic Center. Each panel using a more complex combination of complex ciphers.

The fourth panel has remained elusive for a reason. It is greatly more complex than the others, to solve it, you both need to find the keys for it, what ciphers were used, and you also need to use the answers from the previous three panels as well. Without the first three answers perfect, the fourth remains impossible.

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Posted by on July 6, 2011 in Articles


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166. ‘Clever Hans’ the Mathematical Horse

In the early twentieth century there was a spectacle, a horse called ‘Clever Hans,’ whom the owner claimed could add, subtract, multiply, divide, work with fractions, tell time, keep track of the calendar, differentiate musical tones, and read, spell, and understand German. Truly a spectacle, bolstered by the sudden interest in animal intelligence thanks to the then fairly recent publication of Darwin’s, ‘On The Origin Of Species.’

Propelled by this interest ‘Clever Hans’ quickly gained repute and fame for both himself and his trainer, Wilhelm Van Osten, a mathematics teacher and an amateur, but in this case successful, horse trainer. Van Osten held spectacles for which he never charged entry, he would gather a crowd, ask Hans a question and Hans would tap the answer out until the right number was reached. For example he would ask,’If the eighth day of the month comes on a Tuesday, what is the date of the following Friday?’ The Hans would tap his hoof the requisite number of times(in this case 11).

Question could be submitted either verbally or in written form. The success of the spectacle allowed ‘Hans’ and van Osten to travel widely across Germany and in fact the whole event was featured at one point on page six of the New York Times. Then came queries, exactly how did the horse do it? Due tot he popularity and wide speculation the German board of education put together a committee of 13 people in order to test the scientific claims being made. They were known as the Hans committee. Read the rest of this entry »

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Posted by on July 5, 2011 in Articles, Misconceptions, Trivia


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156. Death by Pi

German mathematician Ludolph van Ceulen spent the majority of his life deriving the digits of pi(π). In 1610 he died of exhaustion after deriving the 35th decimal.

The 35 digits are engraved in his tombstone.

π ≈ 3.14159265358979323846264338327950288

As an aside, we currently know pi to over 2.5 trillion places.

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Posted by on June 25, 2011 in Trivia


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19. The Rubik’s Cornucopia Cube

FACT: There are exactly 43,252,003,274,489,856,000 (43 Quintillion) possible combinations of colours one can make from a single Rubik’s Cube. If there was one Rubik’s Cube for every one of these combinations or permutations then we could form a uniform layer of Rubik’s Cube over the Earth that would be 275 cubes deep, that’s around 20 metres in height.

In April 2010 an International group of Scientists and Mathematicians found that it is possible to solve any Rubik’s Cube in 20 moves or less. That’s about 0.00000000000000216% of all of the possible permutations.

On a final note if you ever look at a Rubik’s Cube in its packaging you may notice that they only say that there are ‘Billions of combinations’ not ‘Quintillions.’ The reason for this is because most people just simply don’t know about numbers that high, in fact the chances are you had never heard of a Quintillion before this. You’re welcome.


Posted by on February 8, 2011 in Articles, Trivia


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