Imagine that a new coin that is worth exactly 13 cents has been introduced to our existing currency system. Prove or disprove the statement:  The cashier’s algorithm using quarters, dimes, nickels, 13-cent coins, and pennies and will produce change using the fewest coins possible for all change values compared to a system without. Provide an example.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Imagine that a new coin that is worth exactly 13 cents has been introduced to our
existing currency system. Prove or disprove the statement: 

The cashier’s algorithm using quarters, dimes, nickels, 13-cent coins, and pennies and will
produce change using the fewest coins possible for all change values compared to a system without.

Provide an example. 

 
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Why would the penny be needed in the case of 36 cents? ( 13 + 13 + 10)

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