3. Schoolchildren were given 7 sheets of paper and asked to cut some of them into 7 pieces. The resulting pieces of paper were mixed and they were asked again to cut some of them into 7 pieces. This was repeated several times. How many pieces of paper need to be cut so that in the end there are 331 pieces.
Solution. After $k$ cuts, there remain $6 k+7$ pieces. Therefore, to determine the number of cuts made, we solve the equation $6 k+7=331 \Rightarrow k=54$.

Answer: 54.