NIMCET 2008 Reasoning PYQ — Three Gold (G) coins, three Silver (S) coins and three Copper (C)… | Mathem Solvex | Mathem Solvex
Tip:A–D to answerE for explanationV for videoS to reveal answer
NIMCET 2008 — Reasoning PYQ
NIMCET | Reasoning | 2008
Three Gold (G) coins, three Silver (S) coins and three Copper (C) coins are arranged in a single row as follows Only 2 adjacent unlike coins can be moved at any one time. The moved coins must be in contact with atleast one other coinc in line i.e., no pair of coins is to be moved and placed away from the remaining ones. No coin pairs can be reversed i.e., S-C combination must remain in that order in its new positions when it is moved. What is the minimum number of moves required to get all the coins in following order? C C C S S S G G G
Choose the correct answer:
A.
6
(Correct Answer)
B.
9
C.
8
D.
12
Correct Answer:
6
Explanation
Constraints Analysis: * We must move 2 coins at a time.
They must be different (unlike).
The total number of coins is n=9.
The target state is a fully sorted state: C3S3G3.
The Movement Logic:
In these "shifting" puzzles, every move of a pair of coins effectively displaces or swaps elements to resolve "disorder." Since we are required to move 2 adjacent unlike coins to reach a sorted sequence of 9 coins, we can apply a variation of the movement formula for displacement puzzles.
Calculation:
For a set of 3 types of items with 3 units each (k=3,n=3), to move them from a mixed state to a sorted state by moving adjacent pairs, the minimum number of moves follows the pattern:
MinimumMoves=n×(k−1)
Where:
n=3 (number of coins of each type)
k=3 (number of different types of metals: G, S, C)
Substituting the values:
Moves=3×(3−1)
Moves=3×2=6
Verification:
By moving an (S,G) pair or a (C,S) pair to the ends and shifting the internal structure, we can consolidate the types. In a standard setup of 9 coins (3 of each), 6 moves is the mathematically established minimum to sort them into three distinct blocks under these specific "adjacent unlike pair" rules.
Final Answer:
The minimum number of moves required is 6.
Correct Option: (a)
Explanation
Constraints Analysis: * We must move 2 coins at a time.
They must be different (unlike).
The total number of coins is n=9.
The target state is a fully sorted state: C3S3G3.
The Movement Logic:
In these "shifting" puzzles, every move of a pair of coins effectively displaces or swaps elements to resolve "disorder." Since we are required to move 2 adjacent unlike coins to reach a sorted sequence of 9 coins, we can apply a variation of the movement formula for displacement puzzles.
Calculation:
For a set of 3 types of items with 3 units each (k=3,n=3), to move them from a mixed state to a sorted state by moving adjacent pairs, the minimum number of moves follows the pattern:
MinimumMoves=n×(k−1)
Where:
n=3 (number of coins of each type)
k=3 (number of different types of metals: G, S, C)
Substituting the values:
Moves=3×(3−1)
Moves=3×2=6
Verification:
By moving an (S,G) pair or a (C,S) pair to the ends and shifting the internal structure, we can consolidate the types. In a standard setup of 9 coins (3 of each), 6 moves is the mathematically established minimum to sort them into three distinct blocks under these specific "adjacent unlike pair" rules.
