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Many modern publishers use a number or letter system to designate first editions. Publishers using this system have numbers or letters similar to 1 2 3 4 5 6 7 8 9 or A B C D E where the 1 or the A indicates a first edition. If the 1 is missing as in 2 3 4 5 6 7 8 9, then that book is probably a second printing, as designated by the remaining 2. Sometimes you´ll find that numbers appear differently or in reverse as in 10 9 8 7 6 5 4 3 2 1. Regardless of the way the numbers look, you want to spot the 1 or the A.
There are exceptions; for example, Random House will use the words First Edition in place of the number 1. Thus a Random House book stating ´First Edition´ starting at the number 2 is first edition, first state book.