Problem:
In a traditional Indian game, players arrange 4 distinct types of coins (gold, silver, bronze, copper) in a row. No two consecutive coins can be the same type. How many unique arrangements are possible?
Solution:
First Coin: There are 4 choices (any type).
Subsequent Coins: For each position after the first, there are 3 choices (excluding the previous coin’s type).
Total Arrangements:
[
4 \times 3 \times 3 \times 3 = 4 \times 3^3 = 4 \times 27 = \boxed{108}
]
Explanation:
The first coin has no restrictions, giving 4 options.
Each subsequent coin must differ from its predecessor, reducing choices to 3 per step.
Multiply the possibilities for each position to get the total unique sequences.
This problem combines combinatorial logic with constraints, typical of strategic Indian games.
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