Page 144 - NUMINO Challenge_C2
P. 144
2 The number of 5's in the numbers from 1 to 999: If the number is 9 , only number that can go
in the is 00, so there is only one 9.
If the number is 5, there are 100 numbers
that can go in the . The total number of 9’s is 90 90 1 181.
If the number is 5 , there are 100 numbers
that can go in the 5 . 3 Divisibility Rules p.24~p.25
If the number is 5 , there are 100 numbers
that can go in the . Example 0 9, 4, 5 450, 540
The numbers of 5’s is 300. TryItAgain If the numbers need to be a multiple of 3,
The numbers that have two 5's: then the sum of the digits must be a
If the number is 55 , there are 10 numbers that multiple of 3. Since 6 3 2 11, the ones
can go in the . digit must be 1, 4, or 7 in order to be a
If the number is 5 5, there are 10 numbers that multiple of 3.
can go in the .
If the number is 55, there are 10 numbers that Example 4 6, 9
can go in the . 6 6
There are 30 numbers that have two 5’s. The TryItAgain A number that is multiple of both 2 and 3 is 6.
number that has three 5’s is 555, only one. Therefore, from 1 to 50, since 50 6 8 r2,
Therefore, there are 300 30 1 271 numbers there are 8 numbers that are multiples of 6.
that have 5's.
Type 3-1 Find a Number that Satisfies the Conditionsp.26~p.27
3 In the numbers from 1 to 77,
1 0, 5
If the number is 7, since numbers from 0 to 7
can go in the , the number of 7’s is 8. In the 2 When 3 is in the hundreds place and 9 is in the
same way, if the number is 7 , since numbers ones place, 3 0 3, then the digits that can go
from 0 to 7 can go in the , the number of 7’s in the tens place are 0, 3, 6, and 9.
is 8. When 3 is in the hundreds place and 5 is in the
ones place, 3 5 8, then the digits that can go
The total number of 7’s is 8 8 16. in the tens place are 1, 4, and 7.
If the number is 3, since numbers from 0 to 7
can go in the , the number of 3’s is 8. In the 3 The greatest number: 390
same way, if the number is 3 , since numbers The smallest number: 300
from 0 to 9 can go in the , the number of 3’s
is 10. 4 The number is a multiple of 4; therefore, the last
two digits must be 00 or a multiple of 4. Also, in
The total number of 3’s is 8 10 18. order to be divisible by 3, the hundreds digit
Therefore, the password is 1618. must be a 3 and the sum of the last two digits
must be a multiple of 3. Therefore, the 2-digit
4 The outcomes in which each number goes either numbers that satisfy the conditions are: 00, 12,
24, 36, 48, 60, 72, 84, and 96, and the greatest
in the ones or tens places are the same. 900 is number is 396.
the only number in which 9 is in the hundreds
place; therefore, the digit 9 is used the least. Answer Key
If the number is 9, since numbers from 00
to 89 can go in the , the number of 9’s is
90.
If the number is 9 , since numbers from 00
to 89 can go in the 9 , the number of 9’s is
90.
in the is 00, so there is only one 9.
If the number is 5, there are 100 numbers
that can go in the . The total number of 9’s is 90 90 1 181.
If the number is 5 , there are 100 numbers
that can go in the 5 . 3 Divisibility Rules p.24~p.25
If the number is 5 , there are 100 numbers
that can go in the . Example 0 9, 4, 5 450, 540
The numbers of 5’s is 300. TryItAgain If the numbers need to be a multiple of 3,
The numbers that have two 5's: then the sum of the digits must be a
If the number is 55 , there are 10 numbers that multiple of 3. Since 6 3 2 11, the ones
can go in the . digit must be 1, 4, or 7 in order to be a
If the number is 5 5, there are 10 numbers that multiple of 3.
can go in the .
If the number is 55, there are 10 numbers that Example 4 6, 9
can go in the . 6 6
There are 30 numbers that have two 5’s. The TryItAgain A number that is multiple of both 2 and 3 is 6.
number that has three 5’s is 555, only one. Therefore, from 1 to 50, since 50 6 8 r2,
Therefore, there are 300 30 1 271 numbers there are 8 numbers that are multiples of 6.
that have 5's.
Type 3-1 Find a Number that Satisfies the Conditionsp.26~p.27
3 In the numbers from 1 to 77,
1 0, 5
If the number is 7, since numbers from 0 to 7
can go in the , the number of 7’s is 8. In the 2 When 3 is in the hundreds place and 9 is in the
same way, if the number is 7 , since numbers ones place, 3 0 3, then the digits that can go
from 0 to 7 can go in the , the number of 7’s in the tens place are 0, 3, 6, and 9.
is 8. When 3 is in the hundreds place and 5 is in the
ones place, 3 5 8, then the digits that can go
The total number of 7’s is 8 8 16. in the tens place are 1, 4, and 7.
If the number is 3, since numbers from 0 to 7
can go in the , the number of 3’s is 8. In the 3 The greatest number: 390
same way, if the number is 3 , since numbers The smallest number: 300
from 0 to 9 can go in the , the number of 3’s
is 10. 4 The number is a multiple of 4; therefore, the last
two digits must be 00 or a multiple of 4. Also, in
The total number of 3’s is 8 10 18. order to be divisible by 3, the hundreds digit
Therefore, the password is 1618. must be a 3 and the sum of the last two digits
must be a multiple of 3. Therefore, the 2-digit
4 The outcomes in which each number goes either numbers that satisfy the conditions are: 00, 12,
24, 36, 48, 60, 72, 84, and 96, and the greatest
in the ones or tens places are the same. 900 is number is 396.
the only number in which 9 is in the hundreds
place; therefore, the digit 9 is used the least. Answer Key
If the number is 9, since numbers from 00
to 89 can go in the , the number of 9’s is
90.
If the number is 9 , since numbers from 00
to 89 can go in the 9 , the number of 9’s is
90.
