Page 142 - NUMINO Challenge_B2
P. 142
Type 1-2 Numbers with Increasing Digits p.12~p.13 Creative Thinking p.14~p.15
1 The tens digit should be greater than the 1 To make the greatest 5-digit number, put the
hundreds digit. Therefore, there are 8 digits, the
numbers are 2, 3, 4, 5, 6, 7, 8, and 9, that can be digits in order from greatest to smallest in the
placed in the hundreds place. corresponding place values. Remember that 0
cannot be in the ten thousands place. Therefore,
2 7 digits (3, 4, 5, 6, 7, 8, 9) the greatest number is 97630, and the second
greatest number is 97603. To make the smallest
3 6 digits (4, 5, 6, 7, 8, 9) 5-digit number, put the digits in order from
smallest to greatest in the corresponding place
4 7 6 5 4 3 2 1 28 values. 0 cannot be in the ten thousands place.
The smallest number is 30679, the 2nd smallest
Problem solving number is 30697, and the 3rd smallest number is
30769.
1 Digits from 2 to 9 can be placed in the hundreds
(2nd greatest number) (3rd smallest number)
place. 97603 30769 66834
When 2 is in the hundreds place:
210 1 number 2 378 378 873 1251 1251 1521 2772
When 3 is in the hundreds place:
321, 320, 310 2 1 3 numbers Step 2 palindromic number
When 4 is in the hundreds place: 831 831 138 969
432, 431, 430, 421, 420, 410
Step 1 palindromic number
3 2 1 6 numbers 264 264 462 726
When 5 is in the hundreds place:
543, 542, 541, 540, 532, 531, 530, 521, 520, 510 726 627 1353
1353 3531 4884
4 3 2 1 10 numbers Step 3 palindromic number
Using the same method, when you add the sum
of the number of the 3-digit numbers for each 3 To make an odd number, 5 or 9 should be in the
condition until when 9 is in the hundreds place,
you get ones place.
1 3 6 10 15 21 28 36 120 numbers. When 5 is in the ones place, 2, 6, 9, or 8 can be
in the hundreds place, and three different
2 When the date is expressed as numbers, the numbers can be in the tens place.
first two digits represent the month and the last 5 4 3 12 odd numbers
two digits represent the day. Since the greatest
number that represents the day is 29, the first When 9 is in the ones place, 5, 2, 6, or 8 can be
two digits should be smaller than 2. Therefore, in the hundreds place, and three different
there are 7 dates (0123, 0124, 0125, 0126, 0127, numbers can be in the tens place.
0128, 0129) that can be represented according
to the given conditions. 9 4 3 12 odd numbers
Therefore, John can make 12 12 24 odd
numbers.
Answer Key
1 The tens digit should be greater than the 1 To make the greatest 5-digit number, put the
hundreds digit. Therefore, there are 8 digits, the
numbers are 2, 3, 4, 5, 6, 7, 8, and 9, that can be digits in order from greatest to smallest in the
placed in the hundreds place. corresponding place values. Remember that 0
cannot be in the ten thousands place. Therefore,
2 7 digits (3, 4, 5, 6, 7, 8, 9) the greatest number is 97630, and the second
greatest number is 97603. To make the smallest
3 6 digits (4, 5, 6, 7, 8, 9) 5-digit number, put the digits in order from
smallest to greatest in the corresponding place
4 7 6 5 4 3 2 1 28 values. 0 cannot be in the ten thousands place.
The smallest number is 30679, the 2nd smallest
Problem solving number is 30697, and the 3rd smallest number is
30769.
1 Digits from 2 to 9 can be placed in the hundreds
(2nd greatest number) (3rd smallest number)
place. 97603 30769 66834
When 2 is in the hundreds place:
210 1 number 2 378 378 873 1251 1251 1521 2772
When 3 is in the hundreds place:
321, 320, 310 2 1 3 numbers Step 2 palindromic number
When 4 is in the hundreds place: 831 831 138 969
432, 431, 430, 421, 420, 410
Step 1 palindromic number
3 2 1 6 numbers 264 264 462 726
When 5 is in the hundreds place:
543, 542, 541, 540, 532, 531, 530, 521, 520, 510 726 627 1353
1353 3531 4884
4 3 2 1 10 numbers Step 3 palindromic number
Using the same method, when you add the sum
of the number of the 3-digit numbers for each 3 To make an odd number, 5 or 9 should be in the
condition until when 9 is in the hundreds place,
you get ones place.
1 3 6 10 15 21 28 36 120 numbers. When 5 is in the ones place, 2, 6, 9, or 8 can be
in the hundreds place, and three different
2 When the date is expressed as numbers, the numbers can be in the tens place.
first two digits represent the month and the last 5 4 3 12 odd numbers
two digits represent the day. Since the greatest
number that represents the day is 29, the first When 9 is in the ones place, 5, 2, 6, or 8 can be
two digits should be smaller than 2. Therefore, in the hundreds place, and three different
there are 7 dates (0123, 0124, 0125, 0126, 0127, numbers can be in the tens place.
0128, 0129) that can be represented according
to the given conditions. 9 4 3 12 odd numbers
Therefore, John can make 12 12 24 odd
numbers.
Answer Key
