The Computer Club of a school has developed a digital treasure-hunt game to help students learn about ancient and modern number systems. Instead of using the usual decimal system, the game records points using a Base-\(8\) (Octal) Number system.
To represent scores, the club uses special symbols:
- Star \(= 1\)
- Triangle \(=8\)
- Square \(= 64\)
Based on this answer the below question:
(i) What is the \(4^{th}\) landmark number in the Base-\(8\) system?
(ii) A student scores a total of \(2\) Square, \(3\) Triangles, and \(2\) Stars points in the game. What is the equivalent score in our standard decimal system?
(iii) If a student scores exactly \(93\) points in decimal system, how would this score represented using the minimum number of Base-\(8\) game symbols?
(iv) The game awards a bonus of \(1\) square whenever player collects \(8\) triangle. How many Squares and Triangles can replace \(18\) Triangles?