# *** Test of Genius "Pt.4" ***?

Steven has 9 gold coins that are

identical in appearance. However, one

coin is counterfeit and weighs slightly

less than the others. Using a balance

scale, how can he find the counterfeit

coin in just two weighings?

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Weighing 1:

Divide the coins in to 3 equal piles of 3 coins.

Weigh 3 coins against 3 coins. If they balance, the counterfeit is in the pile that wasn’t weighed. Otherwise it is in the pile that was lighter on the scale.

Weighing 2:

Take the light pile and weigh two coins. Just like before if they balance the counterfeit is the one that wasn’t weighed. Otherwise it is the one that was lighter on the scale.

Take coins 1-3 and weigh against coins 4-6. If they are equal, the counterfeit is among 7-9. If 1-3 weighs more, the counterfeit is among 4-6, if 1-3 weighs less, the counterfeit is among 1-3. Then take the set of 3 coins you know the counterfeit is among. Weigh two of them against each other. If equal, the counterfeit is the third, and if they are not equal, the counterfeit is the one that weighs less.

Test of genius? As if. I could have solved that when I was 4 years old and I consider myself to be incredibly stupid.

put three coins on one side of the balance, and three on the other.

you know which group of three coins the counterfeit is in because either one side of the balance will be lighter (in which case the counterfeit is there) or it is balanced and the coin is one of the three left out.

take the three coins and put one on each side of the balance. Either one coin will be lighter (ie counterfeit) or the balance will be balanced and the coin left out is counterfeit.

label the coins A B C D E F G H I

weigh ABC : DEF

consider three possibilities:

ABC = DEF then GHI has the fake

ABC < DEF then ABC has the fake

ABC > DEF then DEF has the fake

take the group that has the fake, weigh two of the coins, if one of them is less than the other then that is the fake. if they are the same then the third coin is the fake.

you can not do it. nine is an odd number. to do this, you could only have 4 coins.if you had 4 coins, you would put two on each side. the that weighs less, you take and put one on one end and one on the other. the lighter one is counterfeit.