$\underline{\text { Martynova } H}$.

To play the game of Hat, Nadya wants to cut a sheet of paper into 48 identical rectangles. What is the minimum number of cuts she will have to make if she can rearrange any pieces of paper but cannot fold them, and Nadya can cut as many layers of paper at once as she likes? (Each cut is a straight line from edge to edge of the piece.)

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With each cut, the number of paper pieces can increase by no more than twice. Therefore, after five cuts, you can get no more than 32 pieces, which is not enough.

Six cuts will suffice. For example, you can cut the sheet in half, align the two rectangular pieces and cut them in half again (resulting in four equal rectangles). By continuing to align the obtained parts and cutting them in half, you can get 16 equal rectangles with four cuts. Then, by dividing the entire stack into three equal parts with two cuts, you will get 48 equal rectangles.

## Answer

6 cuts.