ps very unclear

[demoskopico]

A construction company wants to number new houses using digit plates only. If the company puts an order for 1212 plates how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1).



260
440
556
792
1200

[JohnB]

The situation in this question may take a bit of time to understand. Basically, the company is going to use 1,212 digits to label the houses with as many numbers as it can, starting from 1.

So first, how many digits does it take to number all the houses with one-digit numbers? These go from 1 to 9, so 9.

Then, how many digits does it take to number all the houses with two-digit numbers? These go from 10 to 99. To find the number of values between 10 and 99, subtract 10 from 99 but then add one (to account for 10 itself).
99-10+1 = 90. There are 90 two digit numbers. Each one takes 2 digits, so the company uses 180 digits on these houses.

At this point, they have 1212 - 189 = 1,023 digits left. How many three-digit houses can they label with these? 1023/3 = 341.

So the total number of houses = 341 + 99 = 440.