Steven has 9 gold coins that are identical in appearance. However, one coin is counterfeit an weighs slightly less that the others. Using a balance scale, how can he find the counterfeit coin in just two weighings?

Split the coins into three groups, A, B and C consisting of 3 coins in each group.

Weigh: A--B
1. If A=B, the the counterfeit is in group C
Weigh any two coins in group C and figure out the rest.

2. If A≠B, then the counterfeit is in the lighter group.
Weigh any two coins in the lighter group and figure out the rest.

Ah, the "weighty" conundrum! Here's a cunning plan for Steven to unveil that sneaky counterfeit coin in just two weighings:

Step 1: Divide and Weigh:
First, he needs to split the 9 coins into three groups of three, let's call them Group A, Group B, and Group C. Then, Steven should place Group A and Group B onto the balance scale.

Scenario A:
If the scale is perfectly balanced, then the counterfeit coin must be in Group C. He can skip Step 2 and go directly to Step 3.

Scenario B:
If the scale tips, Steven can narrow it down further. If Group A is heavier, the counterfeit coin is either in Group A or Group B. If Group B is heavier, it must be in Group B or Group C.

Step 2: Pinpoint the Culprit:
Steven now knows the potential location of the counterfeit coin. Take the group that is suspected to be the impostor (either Group A or Group C, depending on Scenario B), and divide it into three individual coins. Let's call these coins "X," "Y," and "Z" in Group A or "P," "Q," and "R" in Group C.

Step 3: The "Winning" Weighing:
For the final weighing, here are the possible outcomes:

Scenario a:
If the scale is perfectly balanced, then the counterfeit coin is whichever coin wasn't weighed.

Scenario b:
If one side is heavier, Steven needs to compare two of the coins from the heavier side. If one of them is lighter, then that coin is the counterfeit. If they balance, the remaining, unweighed coin is the sneaky culprit.

And voila! In just two weighings, Steven can expose that mischievous counterfeit coin, all while keeping things perfectly balanced...as all things should be (well, except for that fake coin, of course).

Steven can find the counterfeit coin in just two weighings using the following steps:

1. Divide the 9 coins into three groups of 3 coins each (Group A, Group B, and Group C).

2. Weigh Group A against Group B using the balance scale. There are three possible outcomes:

a. If Group A is lighter, then the counterfeit coin is in Group A.
b. If Group B is lighter, then the counterfeit coin is in Group B.
c. If both groups weigh the same, then the counterfeit coin is in Group C.

3. Take the group that contains the counterfeit coin (identified in step 2) and divide it into three coins (Group D, Group E, and Group F).

4. Weigh Group D against Group E using the balance scale. There are three possible outcomes:

a. If Group D is lighter, then the counterfeit coin is in Group D.
b. If Group E is lighter, then the counterfeit coin is in Group E.
c. If both groups weigh the same, then the counterfeit coin is Group F.

By following these steps, Steven can identify the group and the specific coin that is counterfeit in just two weighings.

To find the counterfeit coin in just two weighings, Steven can follow these steps:

Step 1: Divide the Coins into Three Groups
- First, divide the 9 gold coins into three groups of three coins each. Let's call these groups A, B, and C.

Step 2: Weighing Group A against Group B
- Take group A and group B and place them on opposite sides of the balance scale.
- If the scale is balanced, it means the counterfeit coin is in group C.
- If the scale is imbalanced, it means either group A or group B contains the counterfeit coin.

Step 3: Identifying the Lighter Group
- If the scale is imbalanced, take the group that is lighter (let's say group A) and set one coin aside.
- Take the other two coins from group A and place them on opposite sides of the balance scale.
- If the scale is balanced, then the coin that was set aside is the counterfeit coin.
- If the scale is imbalanced, the lighter coin on the scale is the counterfeit coin.

By following these steps, Steven can find the counterfeit coin in just two weighings using the balance scale.

what if the counterfeit coin is on the heavier side because it would tip the scales if a normal one was on the lighter side and a normal one plus the counterfeit one was on the heavier side