Each piece of type can be used only once.How many twos will he need to number pages 1 through 232?

Its 87 pieces of type

2's in the ones place: 2, 12, 22, 32, ... 232 = 24
2's in the tens place: 20 - 29, 120-129, 220-229 = 30
2's in the hundreds place: 200 - 232 = 33

so 24 + 30 + 33