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Cashier balancing [1] or cashing up is the process of a cashier counting the money in a cash register at the end of a business day or working shift. The process is usually conducted in businesses such as grocery stores, restaurants and banks, and makes the cashier responsible for the money in their cash register.
Another example is attempting to make 40 US cents without nickels (denomination 25, 10, 1) with similar result — the greedy chooses seven coins (25, 10, and 5 × 1), but the optimal is four (4 × 10). A coin system is called "canonical" if the greedy algorithm always solves its change-making problem optimally.
Other examples include counting tiles on the floor or ceiling, the number of lines on the highway, or touching things a certain number of times such as a door knob or a table. Arithmomania sometimes develops into a complex system in which the person assigns values or numbers to people, objects and events in order to deduce their coherence.
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First mechanical means for the sorting and counting of banknotes existed in the 1920s already. In 1916, the USA granted the patent Machine for Assorting and Counting Paper Money. [4] The machine offered several slots for feeding banknotes by a cashier and used mechanical counters.
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