**ANSWER**: For the FIRST weighing, put coins 1, 2, 3, and 4 on one side and coins 5, 6, 7, and 8

on the other side. This will result in one of three scenarios:

**Scenario 1: The scale is lower/heavier on the left.**

You now know that one of the 8 coins being measured is counterfeit. You also know that if the counterfeit

coin is on the left, it is heavier, and if it is on the right, it is lighter. Remaining possibilities for

counterfeit coin: 1H, 2H, 3H, 4H, 5L, 6L, 7L, or 8L. For the SECOND weighing, put coins 1, 3, and 5 on the

left and coins 2, 4, and 6 on the right. This will result in one of three scenarios:

Scenario 1A: The scale is lower/heavier on the left.

This signifies 1H, 3H, 5H, 2L, 4L, or 6L of which only 1H, 3H, or 6L are possible. You now know that the

counterfeit coin is coin 1, 3, or 6. Remaining possibilities for counterfeit coin: 1H, 3H, or 6L. For the

THIRD weighing, put coin 1 on the left and coin 3 on the right. If the scale is lower/heavier on the left,

coin 1 is the counterfeit coin. If the scale is lower/heavier on the right, coin 3 is the counterfeit coin.

If the scale is balanced, coin 6 is the counterfeit coin.

Scenario 1B: The scale is lower/heavier on the right.

This signifies 1L, 3L, 5L, 2H, 4H, or 6H of which only 5L, 2H, or 4H are possible. You now know that the

counterfeit coin is coin 2, 4 or 5. Remaining possibilities for counterfeit coin: 2H, 4H, or 5L. For the

THIRD weighing, put coin 2 on the left and coin 4 on the right. If the scale is lower/heavier on the left,

coin 2 is the counterfeit coin. If the scale is lower/heavier on the right, coin 4 is the counterfeit coin.

If the scale is balanced, coin 5 is the counterfeit coin.

Scenario 1C: The scale is balanced.

You now know that one of the two unweighed coins in the second weighing (coin 7 or 8)is counterfeit.

Remaining possibilities for the counterfeit coin: 7L or 8L. For the THIRD weighing, put coin 7 on the left

and coin 8 on the right. If the scale is lower/heavier on the left, coin 8 is the counterfeit coin. If the

scale is heavier on the right, coin 7 is the counterfeit coin.

**Scenario 2: The scale is lower/heavier on the right.**

You now know that one of the 8 coins being measured is counterfeit. You also know that if the counterfeit

coin is on the left, it is lighter, and if it is on the left, it is heavier. Remaining possibiilties for

counterfeit coin: 1L, 2L, 3L, 4L, 5H, 6H, 7H, or 8H. For the SECOND weighing, put coins 1, 3, and 5 on the

left and coins 2, 4, and 6 on the right. This will result in one of three scenarios:

Scenario 2A: The scale is lower/heavier on the left.

This signifies 1H, 3H, 5H, 2L, 4L, or 6L of which only 5H, 2L, or 4L are possible. You now knoe that the

counterfeit coin is coin 2, 4, or 5. Remaining possibilities for counterfeit coin: 2L, 4L, or 5H. For the

THIRD WEIGHING, put coin 2 on the left and coin 4 on the right. If the scale is lower/heavier on the left,

coin 4 is the counterfeit coin. If the scale is lower/heavier on the right, coin 2 is the counterfeit coin.

If the scale is balanced, coin 5 is the counterfeit coin.

Scenario 2B: The scale is lower/heavier on the right.

This signifies 1L, 3L, 5L, 2H, 4H, or 6H of which only 1L, 3L, or 6H are possible. You now know that the

counterfeit coin is coin 1, 3 or 6. Remaining possibilities for counterfeit coin: 1L, 3L, or 6H. For the

THIRD weighing, put coin 1 on the left and coin 3 on the right. If the scale is lower/heavier on the left,

coin 3 is the counterfeit coin. If the scale is lower/heavier on the right, coin 1 is the counterfeit coin.

If the scale is balanced, coin 6 is the counterfeit coin.

Scenario 2C: The scale is balanced.

You now know that one of the two unweighed coins in the second weighing (coin 7 or 8) is counterfeit.

Remaining possibilities for the counterfeit coin: 7H or 8H. For the THIRD weighing, put coin 7 on the left

and coin 8 on the right. If the scale is lower/heavier on the left, coin 7 is the counterfeit coin. If the

scale is heavier on the right, coin 8 is the counterfeit coin.

**Scenario 3: The scale is balanced**.

You now know that one of unweighed coins is counterfeit (coin 9, 10, 11, or 12). Remaining possibilities

for counterfeit coin: 9H, 9L, 10H, 10L, 11H, 11L, 12H, or 12L. For the SECOND weighing, put coins 1 and 9

on the left and coins 10 and 11 on the right. This will results in one of three scenarios:

Scenario 3A: The scale is lower/heavier on the left.

This signifies 1H, 9H, 10L, or 11L of which only 9H, 10L, or 11L are possible. You now know that the

counterfeit coin is coin 9, 10, or 11. Remaining possibilities for counterfeit coin: 9H, 10L, or 11L. For the

THIRD weighing, put coin 10 on the left and coin 11 on the right. If the scale is lower/heavier on the left,

coin 11 is the counterfeit coin. If the scale is lower/heavier on the right, coin 10 is counterfeit coin.

If the scale is balanced, coin 9 is the counterfeit coin.

Scenario 3B: The scale is lower/heavier on the right.

This signifies 1L, 9L, 10H, or 11H of which only 9L, 10H, or 11H are possible. You now know that the

counterfeit coin is coin 9, 10, or 11. Remaining possibilities for counterfeit coin: 9L, 10H, or 11H. For the

THIRD weighing, put coin 10 on the left and coin 11 on the right. If the scale is lower/heavier on the left,

coin 10 is the counterfeit coin. If the scale is lower/heavier on the right, coin 11 is counterfeit coin.

If the scale is balanced, coin 9 is the counterfeit coin.

Scenario 3C: The scale is balanced.

Coin 12 is the counterfeit coin.

NOTE: The letter H or L next to coin in the scenarios above signify a heavy or light counterfeit coin.

: For the FIRST consider, put coins 1, 2, 3, and 4 on one side and coins 5, 6, 7, and 8 on the other side. This will result in one of three scenarios : You nowadays know that one of the 8 coins being measured is counterfeit. You besides know that if the forge mint is on the leave, it is heavier, and if it is on the right, it is lighter. Remaining possibilities for counterfeit coin : 1H, 2H, 3H, 4H, 5L, 6L, 7L, or 8L. For the SECOND weigh, put coins 1, 3, and 5 on the bequeath and coins 2, 4, and 6 on the right. This will result in one of three scenarios : scenario 1A : The plate is lower/heavier on the left.This signifies 1H, 3H, 5H, 2L, 4L, or 6L of which only 1H, 3H, or 6L are potential. You nowadays know that the counterfeit coin is coin 1, 3, or 6. Remaining possibilities for counterfeit coin : 1H, 3H, or 6L. For the THIRD weigh, put mint 1 on the left and coin 3 on the proper. If the scale is lower/heavier on the exit, coin 1 is the forge coin. If the scale is lower/heavier on the mighty, coin 3 is the counterfeit coin. If the scale is balanced, coin 6 is the forge coin.Scenario 1B : The scale is lower/heavier on the right.This signifies 1L, 3L, 5L, 2H, 4H, or 6H of which entirely 5L, 2H, or 4H are possible. You now know that the counterfeit coin is mint 2, 4 or 5. Remaining possibilities for counterfeit coin : 2H, 4H, or 5L. For the THIRD weigh, put coin 2 on the leave and coin 4 on the mighty. If the scale is lower/heavier on the leave, coin 2 is the counterfeit coin. If the scale is lower/heavier on the correct, coin 4 is the counterfeit coin. If the scale is balanced, coin 5 is the forge coin.Scenario 1C : The scale is balanced.You now know that one of the two unweighed coins in the second weigh ( coin 7 or 8 ) is counterfeit. Remaining possibilities for the forge coin : 7L or 8L. For the THIRD weigh, put coin 7 on the forget and coin 8 on the right. If the scale is lower/heavier on the bequeath, coin 8 is the counterfeit mint. If the scale is heavier on the right, coin 7 is the forge coin.You now know that one of the 8 coins being measured is counterfeit. You besides know that if the counterfeit coin is on the left, it is lighter, and if it is on the left, it is heavier. Remaining possibiilties for counterfeit mint : 1L, 2L, 3L, 4L, 5H, 6H, 7H, or 8H. For the SECOND weigh, put coins 1, 3, and 5 on the leftover and coins 2, 4, and 6 on the right. This will result in one of three scenarios : scenario 2A : The scale is lower/heavier on the left.This signifies 1H, 3H, 5H, 2L, 4L, or 6L of which only 5H, 2L, or 4L are possible. You immediately knoe that the counterfeit mint is coin 2, 4, or 5. Remaining possibilities for counterfeit coin : 2L, 4L, or 5H. For the THIRD WEIGHING, put coin 2 on the exit and coin 4 on the right. If the scale is lower/heavier on the leave, coin 4 is the counterfeit mint. If the scale is lower/heavier on the right, coin 2 is the forge mint. If the scale is balanced, coin 5 is the counterfeit coin.Scenario 2B : The scale is lower/heavier on the right.This signifies 1L, 3L, 5L, 2H, 4H, or 6H of which alone 1L, 3L, or 6H are potential. You nowadays know that the counterfeit coin is coin 1, 3 or 6. Remaining possibilities for counterfeit coin : 1L, 3L, or 6H. For the THIRD weigh, put mint 1 on the left and coin 3 on the correct. If the scale is lower/heavier on the bequeath, coin 3 is the forge mint. If the scale is lower/heavier on the right, coin 1 is the counterfeit coin. If the scale is balanced, coin 6 is the counterfeit coin.Scenario 2C : The plate is balanced.You now know that one of the two unweighed coins in the second deliberation ( coin 7 or 8 ) is counterfeit. Remaining possibilities for the forge mint : 7H or 8H. For the THIRD weigh, put mint 7 on the leave and coin 8 on the correct. If the scale is lower/heavier on the left, coin 7 is the forge coin. If the scale is heavier on the correctly, coin 8 is the forge coin.You now know that one of unweighed coins is forge ( mint 9, 10, 11, or 12 ). Remaining possibilities for counterfeit coin : 9H, 9L, 10H, 10L, 11H, 11L, 12H, or 12L. For the SECOND count, put coins 1 and 9 on the leave and coins 10 and 11 on the proper. This will results in one of three scenarios : scenario 3A : The scale is lower/heavier on the left.This signifies 1H, 9H, 10L, or 11L of which lone 9H, 10L, or 11L are possible. You now know that the counterfeit mint is coin 9, 10, or 11. Remaining possibilities for counterfeit coin : 9H, 10L, or 11L. For the THIRD weigh, put coin 10 on the forget and coin 11 on the right. If the scale is lower/heavier on the leave, coin 11 is the counterfeit coin. If the plate is lower/heavier on the right, coin 10 is counterfeit coin. If the scale is balanced, coin 9 is the counterfeit coin.Scenario 3B : The scale is lower/heavier on the right.This signifies 1L, 9L, 10H, or 11H of which only 9L, 10H, or 11H are possible. You now know that the forge coin is mint 9, 10, or 11. Remaining possibilities for counterfeit mint : 9L, 10H, or 11H. For the THIRD consider, put coin 10 on the leave and coin 11 on the correct. If the scale is lower/heavier on the left, coin 10 is the counterfeit mint. If the scale is lower/heavier on the right, coin 11 is forge coin. If the scale is balanced, coin 9 is the forge coin.Scenario 3C : The scale is balanced.Coin 12 is the counterfeit coin.NOTE : The letter H or L future to coin in the scenarios above signify a heavy or light counterfeit coin.

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