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=                            Tally marks                             =
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                             Introduction
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Tally marks, also called hash marks, are a unary numeral system. They
are a form of numeral used for counting. They are most useful in
counting or tallying ongoing results, such as the score in a game or
sport, as no intermediate results need to be erased or discarded.

However, because of the length of large numbers, tallies are not
commonly used for static text. Notched sticks, known as tally sticks,
were also historically used for this purpose.


                            Early history
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Counting aids other than body parts appear in the Upper Paleolithic.
The oldest tally sticks date to between 35,000 and 25,000 years ago,
in the form of notched bones found in the context of the European
Aurignacian to Gravettian and in Africa's Late Stone Age.

The so-called 'Wolf bone' is a prehistoric artifact discovered in 1937
in Czechoslovakia during excavations at Vestonice, Moravia, led by
Karl Absolon. Dated to the Aurignacian, approximately 30,000 years
ago, the bone is marked with 55 marks which may be tally marks. The
head of an ivory Venus figurine was excavated close to the bone.

The Ishango bone, found in the Ishango region of the present-day
Democratic Republic of Congo, is dated to over 20,000 years old. Upon
discovery, it was thought to portray a series of prime numbers. In the
book 'How Mathematics Happened: The First 50,000 Years', Peter Rudman
argues that the development of the concept of prime numbers could only
have come about after the concept of division, which he dates to after
10,000 BC, with prime numbers probably not being understood until
about 500 BC. He also writes that "no attempt has been made to explain
why a tally of something should exhibit multiples of two, prime
numbers between 10 and 20, and some numbers that are almost multiples
of 10." Alexander Marshack examined the Ishango bone microscopically,
and concluded that it may represent a six-month lunar calendar.


                              Clustering
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Tally marks are typically clustered in groups of five for legibility.
The cluster size 5 has the advantages of (a) easy conversion into
decimal for higher arithmetic operations and (b) avoiding error, as
humans can far more easily correctly identify a cluster of 5 than one
of 10.


File:Tally marks.svg|Tally marks used in most of Europe, Zimbabwe,
Australia, New Zealand and North America. In some variants, the
diagonal/horizontal slash is used on its own when five or more units
are added at once.
File:Tally marks 3.svg|Cultures using Chinese characters tally by