assignment, Theory of Computation

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Consider a water bottle vending machine as a finite–state automaton. This machine is designed to accept coins of Rs. 2 and 5 only. It dispenses a single water bottle as soon as the amount entered is equal to or greater than Rs. 12. Coins may be inserted in any order and the machine returns appropriate amounts of change (Note: it returns a chocolate in place of one rupee change). However, there is no cancel button to get back the coins without completing the transaction. What is the exact number of states needed in this automaton? Show the automaton.

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