Units of paper quantity was ordered by the ream of 480 sheets. In 1840, a ream in Lisbon was 17 quires and 3 sheets = 428 sheets, and a double ream was 18 quires and 2 sheets = 434 sheets; and in Bremen, blotting or packing paper was sold in reams of 300 (20 quires of 15 sheets). A mid-19th century Milanese-Italian dictionary has an example for a "risma" (ream) as being either 450 or 480 sheets. In the UK in 1914, paper was sold using the following reams: Reams of 500 sheets were mostly used only for newsprint. Since the late 20th century,
Many-one reduction problem is easy to solve. The many-one reduction is more effective at separating problems into distinct complexity classes. However, the increased restrictions on many-one reductions make them more difficult to find. Many-one reductions were first used by Emil Post in a paper published in 1944. Later Norman Shapiro used the same concept in 1956 under the name "strong reducibility". Suppose "A" and "B" are formal languages over the alphabets Σ and Γ, respectively. A many-one reduction from "A" to "B" is a total computable function "f" : Σ → Γ that has the property that each word "w" is in