Problem 35. The sum of all digits

What is the sum of all the digits (not the numbers) in the sequence 1, 2, 3, 4, 5, 6, 7, ..., 999, 1000?

Problem 34. Barrels

There are 21 barrels such that 7 of them are empty, 7 are half full with orange juice and 7 are full with orange juice. One needs to load this barrels into 3 trucks so that barrels and juice are divided equally between trucks. How can he do that?

Problem 33. 100 pieces

Anne and Bob are tearing up a sheet of paper. Anne only tears a piece of paper into 3 smaller pieces while Bob only tears a piece of paper into 5 smaller pieces. After a few minutes can there be exactly 100 pieces of paper?