부산대학교 도서관

Authors' introduction and summary: ``The general principle of the lotto problem is as follows. A lotto form contains a sequence of the $n$ first integers. Filling a form consists in choosing $k$ numbers in this sequence. $l$ numbers are chosen (without replacement) by the `national lottery' and a 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. The choice of $n$, $k$, $l$ and $t$ is not the same for each country. For example, in Belgium, $n=40$, $k=l=6$, $t=3$. The `lotto problem' asks the following question: `What is the minimal number of lotto forms to be filled in to be sure of obtaining a prize, whatever the drawing?' \par ``The lotto problem generalizes the covering problem and the so-called Turán problem. We present original results concerning lower and upper bounds to the lotto number.''