Page 54 - NUMINO Challenge_D1
P. 54
Basic Concepts Using the Balance the Least Number of Times
Out of these four gold coins, the one fake coin weighs the least. When you
measure the weight of the coins at a time on the balance, the following three
cases can occur. 2 1 21 2
1
3 33
4 44
In the case of Balance , the fake coin is 2 , and in the case of balance
, the fake coin is 1 . In the case of Balance , the coins 3 and 4
need to be compared again to identify the fake coin. Therefore, in order to
find the fake coin among the four coins, the least number of times you must
use the balance is 2.
Example Out of these nine gold coins, the one fake coin weighs the most,
and the other eight coins weigh the same. What is the least
number of times you must use the balance to find the fake coin?
Class Notes
Divide the nine gold coins into three groups.
(1 2 3) ( 4 5 6) (7 8 9)
When you measure groups and on the balance, the following three cases can
occur.
The fake gold coin is in group .
The fake gold coin is in group .
The fake gold coin is in group .
Since there are three gold coins in each group, using the answers from , the balance
must be used at least times to identify the fake gold coin.
51Words and Logic
Out of these four gold coins, the one fake coin weighs the least. When you
measure the weight of the coins at a time on the balance, the following three
cases can occur. 2 1 21 2
1
3 33
4 44
In the case of Balance , the fake coin is 2 , and in the case of balance
, the fake coin is 1 . In the case of Balance , the coins 3 and 4
need to be compared again to identify the fake coin. Therefore, in order to
find the fake coin among the four coins, the least number of times you must
use the balance is 2.
Example Out of these nine gold coins, the one fake coin weighs the most,
and the other eight coins weigh the same. What is the least
number of times you must use the balance to find the fake coin?
Class Notes
Divide the nine gold coins into three groups.
(1 2 3) ( 4 5 6) (7 8 9)
When you measure groups and on the balance, the following three cases can
occur.
The fake gold coin is in group .
The fake gold coin is in group .
The fake gold coin is in group .
Since there are three gold coins in each group, using the answers from , the balance
must be used at least times to identify the fake gold coin.
51Words and Logic
