9. The houses on the south side of Crazy Street are numbered in increasing order starting at 1 and using consecutive odd numbers, except that odd numbers that contain the digit 3 are missed out. What is the number of the 20th house on the south side of Crazy Street?
A 41
B 49
C 51
D 59
E 61
Solution
D

The house numbers on the south side of Crazy Street are consecutive odd numbers apart from any which contain the digit 3 . Therefore the numbers start $1,5,7,9,11,15,17,19$, etc. It can be seen that the tens digit increases every four houses. Hence the 20th house would be the last house of the fifth group of four houses. Since no house numbers contain the digit 3, there is no group of houses whose house numbers start with a 3 and hence the numbers in the fifth group of four houses start with a 5 . Therefore the number of the 20 th house is 59 .