1. What digit does $1 \cdot 2 \cdot \ldots \cdot 99-1 \cdot 3 \cdot 5 \cdot \ldots \cdot 99$ end with?
Solution. $1 \cdot 2 \cdot \ldots .99$ has a ten in the multiplication and therefore ends in 0. The number $1 \cdot 3 \cdot 5 \cdot \ldots .99$ is odd because all are odd and has a five in the product, so it ends in 5. Therefore, the given product $1 \cdot 2 \cdot \ldots .99 - 1 \cdot 3 \cdot 5 \cdot \ldots .99$ ends in 5.