8.1. There are 15 rectangular sheets of paper. In each move, one of the sheets is chosen and divided by a straight cut, not passing through the vertices, into two sheets. After 60 moves, it turned out that all the sheets are either triangles or hexagons. How many hexagons?
Answer: 25

Solution. Let after 60 cuts, $x$ hexagons and $75-x$ triangles are formed (there were 15 sheets, and with each cut, the number of sheets increases by 1). Now let's count the number of sides. Initially, there were $15 \cdot 4=60$ sides, and with each cut, the number of sides increases by 4 (the cut divides two sides of the sheet in half, and also counts as a side in the two new sheets). After 60 cuts, we get 300 sides. Knowing how many sides each triangle and hexagon has, we get $300=3(75-x)+6 x$, from which $x=25$.