A new subdivision is being constructed, along a long road with hundreds of houses. The houses are all numbered in order starting with 1 – so they proceed 1, 2, 3, 4, … down the long road. All of the people go to the hardware store to buy numbers for their mailbox, and they line up in order at the counter. The store, unfortunately, has only 100 of each digit available.

Which homeowner will be the first who cannot buy the complete number for his mailbox?

(In reply to Numbers by jono)

Say what? I counted all the 10 1s used as ones place digits, and 10 1s in the 10s place digits. 11 counts twice because it fits both criteria.

There are 20 already, so every number you count past adds 1, and every one that ends in 1 counts and every 110-119 counts 1. So for 1-99 plus 100-119, there are 20+20+10+2 or 52 numbers. Then from 120-162 there are 43 numbers (hundreds-place 1s), and 5 ones-place 1s. which makes a total of 100 1s.

Which means the first number after this that uses a 1 is 163, which is the answer.

Posted by Gamer on 2003-06-18 12:30:56