Covering With N-staircase

Covering in Combination of Geometry has been one of the most prevailing questions in High School Mathematics Competition. Covering with n×m rectangle is the main materials of this kind questions while it seldom refers to n-staircase covering which is researched in details in the paper according to the covering questions in recent year competitions.The whole article can be divided into several parts:a. The basic methods of covering.b. Four different kinds of n-staircase covering questions:complete covering with the same figure, complete covering with different figures, incomplete covering and saturated covering.c. Eight propositions are given on the four kinds of n-staircase covering on the basis of n×m rectangle covering..d. Five mathematical Olympiad questions are designed on n-staircase covering.According to the content of mathematic competition, n-staircase covering, a kind of typical question, is studied which is also beneficial for connecting the research of mathematic competition with middle school teaching. This article has two innovative aspects:a. Eight propositions are given according to n×m rectangle covering.b. Five mathematic Olympiad questions are designed according to rearranging some covering questions in latest competitions based on n-staircase.