Question

On a huge site in San-Diego the whole new street of houses was constructed. To put the numbers on all new buildings the plates with the digits were used. How many of those plates will be used on the left side of the street with odd numbers and how many plates will be used for the right side of the street with even numbers only, if numeration started from #1 up to #99? How many houses on each side of the street?

Answer 1

There are 45 houses on the left and require 95 plates, while there are 44 houses on the right and require 94 plates

Explanation:

Houses are numbered from 1 to 99. So, there are 99 houses. Odd-numbered houses are on the left. So, there are 50 houses on the left, while there are 49 houses on the right.

For houses on left : The houses are numbered 1, 3, 5, 7, 9, 11, 13..... 97, 99

So 5 houses( 1, 3, 5, 7, 9) require only one plate for numbering, while the remaining 45 houses require 2 plates each. So total number of plates =
`5\textrm{x}1+45\textrm{x}2` =
`95` plates.

For houses on right : The houses are numbered 2, 4, 6, 8, 10, 12, 14.... 96, 98

So 4 houses( 2, 4, 6, 8) require only one plate for numbering, while the remaining 45 houses require 2 plates each. So total number of plates =
`4\textrm{x}1+45\textrm{x}2` =
`94` plates.

∴ There are 45 houses on the left and require 95 plates, while there are 44 houses on the right and require 94 plates.