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Three Weighty Coins Solution

Question: You have 3 coins. Two are of the same weight, and one is different (either heavier or lighter). How can you identify the odd coin using just one weighing?

Solution:

  1. Weigh Coin 1 against Coin 2.

There are two possible outcomes:

  • Outcome 1: The scale balances.

    • If the scale balances, it means that Coin 1 and Coin 2 are of the same weight, so the odd coin must be Coin 3.
    • Since Coin 3 is the odd one out and we don’t know if it’s heavier or lighter, it is indeed different from Coins 1 and 2.

  • Outcome 2: The scale tips.

    • If the scale tips, it means that Coin 1 and Coin 2 are not of the same weight, and one of them is the odd coin.
    • The odd coin will be either heavier or lighter depending on which side of the scale is lower.

Analysis:

  • Single Weighing Strategy:

  • By weighing two coins against each other, you can determine which coin is different by elimination. If the scale is balanced, the unweighed coin is the odd one. If the scale tips, you know which two coins are different and which one of those is odd.

  • Why This Works:

  • There are only three coins, so by weighing two of them, you immediately identify the odd coin (whether it’s heavier or lighter) based on the scale’s reaction. This direct approach takes advantage of the simplicity of the puzzle and provides a clear answer with minimal information.

This simple logic puzzle demonstrates how even a minimal number of items can be efficiently handled with basic logical deduction.

Technique Used for the 3 Coins Puzzle

Technique: Direct Comparison with Elimination

1. Direct Comparison: - The technique involves using a balance scale to directly compare two of the three coins. This comparison provides immediate information about which coins are equal in weight and which one is different.

2. Elimination: - By comparing two coins, you either find out that they are the same (and hence the odd coin must be the one not weighed) or determine which of the two coins is odd if the scale tips.

Detailed Steps:

  1. Weigh Coin 1 against Coin 2.

  2. Outcome 1: The scale balances.

    • Analysis: Coin 1 and Coin 2 are the same weight, so Coin 3 is the odd one out. Since Coin 3 was not weighed, it is automatically identified as the different coin.

  3. Outcome 2: The scale tips.

    • Analysis: Coin 1 and Coin 2 are different. The odd coin is identified between these two based on which side of the scale is heavier or lighter.

Why This Technique Works:

  • Simplicity: With only three coins, weighing two directly gives you the information needed to pinpoint the odd coin with just one weighing.
  • Efficiency: The direct comparison method eliminates the need for multiple weighings or additional steps, making it the most efficient solution for this puzzle.

This technique effectively uses the balance scale to immediately narrow down the possibilities and identify the odd coin through a process of elimination.