| Version 3 ( Case 2) | Use A, B ,C and D to represent groups of three coins | Rational |
| First weighing | Place A and B on either side of the scale. | If the scale does not balance, try by replacing A with C. |
| Second weighing | Replace A with C | If it is also unbalanced, counterfeit is in B. |
| 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. |
| Version 3 ( Case 3) | 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 does not balance, try by replacing B with C. |
| Second weighing | Replace B with C | If it is also unbalanced, counterfeit is in A. |
| 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. |
Done by: Jin Yuan 3E1 (41)
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