The puzzle is determined by the transactions being sent at the time and the previous puzzle solution. This means the solution to one puzzle is always different from the puzzles before. Attempting to change an earlier transaction, maybe to fake bitcoins being sent or change the number of someone's bitcoins, requires solving that puzzle again, which takes a lot of work, and also requires solving each of the following puzzles, which takes even more work. This means a bitcoin cheater needs to outpace all the other bitcoin miners to change the bitcoin history. This makes the bitcoin blockchain very safe to use.