Compete · Slovenia
Drzavno tekmovanje (national round) 2002
1The smallest natural number whose square ends in three fours is \(38\), because \(38^2 = 1444\). Which natural number is the next smallest one with this property?2Tine collects stamps. For his birthday he received a new album with room for plenty of them, so he took \(2002\) tolars out of his money box and decided to spend all of it on stamps. A friend offered him …3Let \(M\) be the midpoint of the base \(AB\) of a trapezoid \(ABCD\), so that \(AB \parallel CD\). A point \(E\) is taken in the interior of the segment \(AC\) in such a way that the lines \(BC\) and \(ME\) …4Stars are drawn in the cells of a \(4 \times 4\) table, at most one star per cell. What is the least number of stars for which the following holds: whichever \(2\) rows and whichever \(2\) columns are …
Work through the paper in order - each problem opens in the workspace with this paper as its trail.