Page 53 - NUMINO Challenge_D1

6 Fake Gold Coins and Balances

Basic Concepts Fake Gold Coins and Balances

"Finding Fake Gold Coins" is a problem solved using the fact that fake gold

coins weigh differently from real gold coins of the same shape and size. It

may be difficult to tell fake and real gold coins apart just by observation, but

it is easy to identify a fake gold coin by using a balance.

Out of these three gold coins( 1 , 2 , 3 ), the one fake coin weighs the

least. When you place coins 1 and 2 on the balance, the following three

cases can occur. 2 21

1 1 2

In the case of Balance , coin 3 is fake.
In the case of Balance , coin 2 is fake.
In the case of Balance , coin 1 is fake.

Example Out of these eight gold coins, the one fake coin weighs the most.
Look at the balances below and find the fake coin.

123 368 23 58

456 457

Class Notes

In the case of Balance , the fake coin is among the coins , , and .

In the case of Balance , the fake coin is among the coins , , and .

In the case of Balance and , the only coins that could be fake are and .
In the case of Balance , 2, 3, 5, and 8 are (fake, real) gold coins.
Therefore, the fake gold coin is .

50 NUMINO Challenge D1