In a building there are 100 rooms. Peter was asked to paint numbers 1 to 100 on the doors. If so, how many times will Peter have to paint the number seven?
please help
Answers
Peter will have to paint the number seven twenty-one times.
Given:
In a building, there are 100 rooms. Peter was asked to paint numbers 1 to 100 on the doors.
To find:
How many times will Peter have to paint the number seven?
Solution:
To determine how many times Peter will have to paint the number seven, count the occurrences of the digit seven from 1 to 100.
Occurrences of 7 can be done in the following cases
Case 1: 7 as single digit
There will be one 7 between 1 to 10
Case 2: Counting occurrences of the digit seven in the units place:
From 1 to 100, there are 10 numbers (7, 17, 27, ..., 97) that have seven in the unit's place.
Case 3: Counting occurrences of the digit seven in the tens place:
From 1 to 100, there are 10 numbers (70, 71, 72, ..., 79) that have seven in the tens place.
Hence,
Peter will have to paint the number seven 10 + 10 + 1 = 21 times in total.
Therefore,
Peter will have to paint the number seven twenty-one times.
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