The people living on Street 'S' of Y-City all decide to buy new house numbers so they line up at the only Hardware store in order of their addresses 1, 2, 3, ... If the store has 100 of each digit, what is the first address that won't be able to buy the digits for its house number?

The digit 1 is used up first. From 1 to 99 it is used 20 times (10 in the units place, 10 in the tens place). From 100 to 162 it appears 63 times in the hundreds place, 10 times in the tens place (110 to 119) and 7 times in the units place (101, 111, ..., 161), a total of $$20 + 63 + 10 + 7 = 100$$. All hundred 1s are gone after 162, so address 163 cannot be made.