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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

Emperor Commodus, on that particular day, was in the mood to see fight unto death dual ‘muneras’ (gladiator fights with only two gladiators at a time where only one of them who was left alive after the fight was declared the winner) on the Colosseum Arena. After the first change in the code from the initial, only two doors would be opened and the respective gladiators behind the doors had to fight. After the second step of change in code, only one gladiator would come out of the opened door and fight the winner of the previous fight. And so on, until the final winner out of the five gladiators was left on the Colosseum Arena. Assuming that the opening or closing of the doors of the gates having no gladiator behind them was inconsequential, what was the minimum number of steps needed to be implemented by Emperor Commodus on that particular day to judge the final winner of the fight unto death dual ‘muneras’ at the Colosseum Arena ?

 

Option: 1

1


Option: 2

2


Option: 3

3


Option: 4

4


Answers (1)

Let us judge this by a practical example :

Initial : C (Spartacus) A (Crixus) C (Maximus) A (Flamma) C (Tetraites)

Step 1 : A (Spartacus) C (Crixus) C (Maximus) A (Flamma) C (Tetraites)

(Munera of Spartacus with Flamma)

Step 2 : A (nil) C(Crixus) A (Maximus) C (nil) C (Tetraites)

(Munera of Maximus with winner of first duel)

Step 3 : A (nil) A (Crixus) C (nil) C (nil) C (Tetraites)

(Munera of Crixus with winner of second duel)

Step 4 : A (nil) A (nil) C (nil) A (nil) A (Tetraites)

(Munera of Tetraites with winner of third duel, and emergence of the final winner)

Hence, it can be clearly understood that irrespective of the order of implementation of the steps, the minimum number of steps that needed to be implemented by Emperor Commodus on that particular day to judge the final winner of the fight unto death dual ‘muneras’ at the Colosseum Arena was 4



 

Posted by

Kshitij

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