Question
Download Solution PDFIf you write down all the numbers from 1 to 100, how many times will you write the number 7?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
We need to consider the digit 7 appearing in the units place and the tens place.
Occurrences in the units place:
The numbers where 7 appears in the units place are: 7, 17, 27, 37, 47, 57, 67, 77, 87, 97.
There are 10 such numbers.
Occurrences in the tens place:
The numbers where 7 appears in the tens place are: 70, 71, 72, 73, 74, 75, 76, 77, 78, 79.
There are 10 such numbers.
Notice that the number 77 has the digit 7 in both the units and the tens place. We have counted it once in the units place list and once in the tens place list.
Total number of times the digit 7 appears = (Occurrences in units place) + (Occurrences in tens place)
Total = 10 + 10 = 20
∴ The number 7 will be written 20 times when writing down all the numbers from 1 to 100.
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