There are 15 gold coins. One of the gold coins is a fake. A fake gold coin is lighter than a real one. You have a “balance machine” without any scale. Can you identify the fake coin by using the “balance machine” at most three times?

Guest Apr 6, 2021

#1**+2 **

Yes you can....is that what you wanted.....or an explanation as to how?

Starts this way make 3 piles 7 7 1

balance the 7's if they balance, then the '1' is the fake

if they DON't balance, the lighter 7 has the fake

take the lighter 7 make 3 piles 3 3 1

balance the 3's if they balance then the '1' is the fake

if they don't balance then the lighter 3 has the fake

take the lighter 3 make 3 piles 1 1 1

balance two of the 1's

if they balance , the third '1' is the fake

if they don't balance , the lighter one is the fake .....with only THREE balances done !

ElectricPavlov Apr 6, 2021

#1**+2 **

Best Answer

Yes you can....is that what you wanted.....or an explanation as to how?

Starts this way make 3 piles 7 7 1

balance the 7's if they balance, then the '1' is the fake

if they DON't balance, the lighter 7 has the fake

take the lighter 7 make 3 piles 3 3 1

balance the 3's if they balance then the '1' is the fake

if they don't balance then the lighter 3 has the fake

take the lighter 3 make 3 piles 1 1 1

balance two of the 1's

if they balance , the third '1' is the fake

if they don't balance , the lighter one is the fake .....with only THREE balances done !

ElectricPavlov Apr 6, 2021