| Version 2 (Case 2) | | Rationale |
| First weighing | Put any 3 coins on either side of the scale. | If the scale is not balanced, the counterfeit is in the heavier side. |
| Second weighing | Place any 2 coins from the heavier group , each on either side of the scale. | 1) If the scale balances, the counterfeit is the last coin. 2) If they do not balance, the heavier coin is the counterfeit. |
| Version 3 ( Case 1) | Use A, B ,C and D to represent groups of three coins | Rationale |
| First weighing | Place A and B on either side of the scale. | If the scale balances, try by replacing B with C. |
| Second weighing | Replace B with C | If it also balances, counterfeit is in D |
| Third weighing | Place any 2 coins, each on either side of the scale | If it does not balance, replace 1 coin with the last coin. |
| Fourth weighing | Replace 1 coin with the last coin. | 1) If the scale balances, counterfeit is the coin that was replaced. 2)If the scale becomes unbalanced(meaning that the other two are equal in weight), counterfeit coin will have a different weight compared to the other 2. |
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