In an absolute numeration system, counts are represented by symbols that have the same value no matter where they appear. The count represented by the numeral is obtained by adding the value of each symbol that forms the numeral. A symbol for a count of zero is not needed. Historically, absolute systems were invented BEFORE place value systems were invented. This suggests that, for teaching practice, students be exposed to an absolute system before they learn our base 10 place value system. A place value system is much more difficult to understand (but the numerals are easier to work with). Many absolute systems have been invented. The Egyptian hieroglyphic system is probably the most well-known absolute numeration system. Shown below are the first twenty numerals of the Egyptian heiroglyphics numeration system (circa 2000 BCE). Notice that two symbols are used: a vertical line (actually a staff) and a horseshoe (actually a heel mark). The staff represents a count of one. The heel symbol represents a count of ten. The reason for ten as the value has nothing to do with place value. It has to do with saving "ink". If new symbols were not invented that represented a group of lower level symbols, then very many symbols would be needed to represent large counts. For example, if no new symbols were invented in the Egyptian system, then writing "two-hundred and twelve" would require making two-hundred and twelve staffs. Clearly, this is not a good solution to representing counts. The Egyptians compressed at ten. That is to say, ten was the count they used to bundle or group lower level symbols. Thus: What Hindu-Arabic number (our modern system) is represented by each of the following Egyptian hieroglyphic numerals?