Page 152 - NUMINO Challenge_D1

Type 6-1 Finding the Different Marble p.52~p.53 Type 6-2 Using the Balance the Least Number of Times p.54~p.55

1 28 g 1 1st Time 2nd Time 3rd Time Fake Coin
2 12 g, 10 g, 7 g

3 Out of ! , " , and $ , there are marbles
that weigh 10 g and 12 g. Therefore,
weighs 7 g.
, , #, %, &

46 46 3

5 ,, 2 3.00
6 10 g : , 12 g :

Problem solving Problem solving

1 On balance , the marbles that weigh 18 g and 1 On balance , notice that # and $ are real,

13 g are among , % , and ' . On balances and on balance , and are fake.
and , and ' are leaning towards the Therefore, a fake coin is heavier than a real coin.

lighter side, so they do not weigh 18 g. 2 Divide the coins into three groups to find the
Therefore, % weighs 18 g.
fake coin by using the balance the least number
2 On balances and , the gold coins 2 , 3 , of times. To find the heaviest coin among 30
coins, first divide them into three groups of ten
4 , 5 , 6 , 8 , 9 , and 10 are coins each. Use the balance once to find which
light coins. Therefore, the heavier coins are 1 group has the heaviest coin. Since there are 10
and 7 . coins in each group, divide the group of ten
coins with the heaviest coin into three groups,
and use the balance more 3 times to find out
which coin is the heaviest. You need to use the
balance at least 4 times. The least numbers of
times are shown in the table below.

Number of Coins 2~3 5~9 10~27 28~81
12 3 4
Number of Times
the Balance Is Used

Answer Key