## Think and solve!
With this issue we start publishing problems traditionally offered
to readers of the traditional
The problems are always published with a solution, hidden somewhere
in the same issue of the journal. However, we will not provide
solutions here. Try for yourself. And if you really cannot find
anything and you are sure you do not want to continue trying,
but you still wish to know the solution, write to pawelst@mimuw.edu.pl or
bartol@mimuw.edu.pl
and ask for one. In order to make our communication easier, we
preserve the original numbers of the problems as they appeared
in
We start with three mathematical problems by M 804. In the small lost-in-the prairies town of Milky Cow 100 cowboys visit 100 local milk saloons every evening. Each of the cowboys chooses the place to spend the night over a pint of milk at random and independently of his colleagues' choices. The town sheriff intends to ban milk products in Milky Cow under the pretext that, anyway, most of the night 3/4 of the saloons remain empty. Milk-loving reader, please prove that the sheriff is wrong! M 805. As a result of acute milk-hunger, sheriff's brain has produced a new illusion. This time our guardian of the law claims that most cowboys drink alone, which aggravates their addiction. Is he right? M 806. In order to bring down the demand for milk in Milky Cow the sheriff decided to introduce drastic new laws. Now the distance between two saloons must be greater than 250 m., whereas the distance between any saloon and the one and only local prison must be less than 1 km. Is there enough room in town for 100 legal saloons? |