Question

Please help me im having my midterm please

Find the Fake Coin. You have eight coins. They all look identical, but one is a
fake and is slightly lighter than the others. Explain how you can use a balance scale to determine which coin is the fake in exactly

a. three weighings.

b. two weighings

Answer 1

Answer:

here

Step-by-step explanation:

hope it will help uh

Answer 2

For identifying fake coin in 3 weighing weigh 8 (4 - 4) , 4(2 - 2) and 2 (1-1) coins.

For identifying fake coin in 2 weighing weigh 6 coins (3 - 3)  first and then based on result weigh  2  (1-1) coins out of these 3 lighter coins or 2  (1-1) left coins if 6 coins weigh equal

Given:

• 8 Coins
• one Fake coin
• Fake Coin is slighter lighter
• use a balance scale

To Find:

• Fake Coin  in
• 3 Weighing
• 2 Weighing

Solution:

3 Weighing

1st Weighing

Put 4 Coins  on Each side

Take 4 Coins which weigh lighter

2nd Weighing

Put 2 Coins  on Each side

Take 2 Coins which weigh lighter

3rd Weighing

Put 1 Coin   on Each side

The one coin which weigh lighter is FAKE

2 Weighing

1st Weighing

Put 3 Coins  on Each side leaving 2 coins

There may be 2 Cases here :

Case 1:  Both Side Weigh Equal

Case 2 : One side is lighter

Case 1: 2nd Weighing

Put 1 Coin   on Each side from remaining 2 coins

The one coin which weigh lighter is FAKE

Case 2 : 2nd Weighing

Put 1 Coins  on Each side leaving one from 3 coins which were lighter

If Both coins weigh Eual Then remaining coin is Fake

If one coin weigh less then that is Fake coin

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