부산대학교 도서관

Authors' introduction and summary: ``The general principle of the lottoproblem is as follows. A lotto form contains a sequence of the $n$ firstintegers. Filling a form consists in choosing $k$ numbers in this sequence.$l$ numbers are chosen (without replacement) by the `national lottery' anda prize is won if at least $t$ of the $l$ numbers belong to the form of $k$numbers. Evidently a player may fill in as many forms as he wants. Thechoice of $n$, $k$, $l$ and $t$ is not the same for each country. Forexample, in Belgium, $n=40$, $k=l=6$, $t=3$. The `lotto problem' asks thefollowing question: `What is the minimal number of lotto forms to be filledin to be sure of obtaining a prize, whatever the drawing?'\par``The lotto problem generalizes the covering problem and the so-calledTurán problem. We present original results concerning lower and upperbounds to the lotto number.''