# How many '7' in a range from '1' to '100'

This question appears on my daughter's Mathematics class in secondary school:

"There are 100 rooms in a hotel. Joe must number the rooms from 1 to 100 with plastic digits. How many times does he need the digit 7?"

My answer is: 07 17 27 37 47 57 67 77 87 97

Number 7 will appear 11 times. However, the book's answer on the back is: 20 times Can you explain why??

• $70, 71, 72, \cdots , 79$ – Simon S Nov 7 '15 at 20:26
• OMG! You right. I feel sooo stupid now. How I could omit them? – Adam Nov 7 '15 at 20:52
• We can close this topic now I guess. thanks a lot. – Adam Nov 8 '15 at 21:10
• Probably not a hard problem, but definitely a great father. – linear_combinatori_probabi Apr 4 '18 at 14:32