In the old days, type was set by hand with lead pieces. Each individual letter or number in each word had to?

Question

be carefully put together. A printer wanted to print a list of whole numbers from 1 to 1000. If he had only 100 of each of the digits from 0 to 9, how many numbers could he set before he ran out of some digit?

Answer 1

From 1-9, you'd use one of each number except zero, so you'd be left with:

0 100
1 99
2 99
3 99
4 99
5 99
6 99
7 99
8 99
9 99

From 10-99, you'd use 9 of each digit including 0 for the 1s digits. Then you'd also need 10 of each digit from 1-9, so you'd use 9 0s and 19 1s, 19 2s, etc.

0 91
1 80
2 80
3 80
4 80
5 80
6 80
7 80
8 80
9 80

Then you're gonna run into a problem with 1s, because you'd need more than 100 1s just to get from 99 to 199. You've only got 80. So you can stop worrying about all the numbers except 1.

From 100-109 you'd use 11 1s, leaving you with 69.

From 110-119 you'd use 21 1s (10 for first digit, 10 for second, 1 for third), leaving you with 48.

From 120-129 you'd use 11 1s, leaving you with 37.

From 130-139 you'd use 11 1s, leaving you with 26.

140-149 you'd use 11 1s, leaving you with 15.

150-159 you'd use 11 1s, leaving you with 4.

160 3 left
161 1 left
162 0 left

So I think 162 is as high as you can go.

This is the 3rd answer I've come up with though. :c) But I feel best about this one.