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  • Directions for question Under the reign of the Roman emperor Commodus in 600 C.E., ‘munera’s, or gladiator fights, held in the Colosseum Arena in Rome were a

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Under the reign of the Roman emperor Commodus in 600 C.E., ‘munera’s, or gladiator fights, held in the Colosseum Arena in Rome were a very common occurrence.

The entrance to the Colosseum Arena by the gladiators took place through five underground corridors opening out to five gates with doors arranged in a row. On one day of the gladiator fight, five infamous gladiators – Spartacus, Crixus, Maximus, Flamma and Tetraites – were to enter the arena through the gates, from left to right respectively, in that order. He whose door was opened had to step out on the arena and fight. Who of the gladiators would fight who depended entirely on the fancy of Emperor Commodus, who controlled the opening or closing of doors using a system of codes. More than two gladiators could fight each other in the arena.

If the door to a gate was to be opened, the code was A (A for Aperio in Latin or open), and if the door to a gate was to be closed, the code was C (C for Clausula in Latin or close). Thus if Emperor Commodus finally stopped at the code ACACC, it meant that he wanted the doors of the first and third gate from the left to the right to be opened, that is Spartacus and Maximus should fight.

On that particular day Emperor Commodus started when the code was initially set at CACAC. He could change the code, but only by using some number of steps, wherein in each step the state of only two consecutive doors could be changed. However he had to reach his desired code using the minimum number of steps. At least one change was mandatory.

Question

On some other day, Emperor Commodus started when the code was initially set at CACAC. He could still change the code as usual by using some number of steps, but this time in each step the state of only two, but any two, doors could be changed. How many distinct gladiator fights could Emperor Commodus initiate at the Colosseum Arena on that other day in a single move ?

 

Option: 1

4


Option: 2

8


Option: 3

10


Option: 4

12


Answers (1)

best_answer

On that other day Emperor Commodus started when the code was already set at CACAC. 

Hence, because this time in each step the state of only two, but any two, doors could be changed in a single move, the number of distinct gladiator fights Emperor Commodus could initiate at the Colosseum Arena, that is choose to change the state of any two doors = 5C2 ways = 10 ways 


 

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Sayak

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