What is the last digit of the product of all odd numbers from 1 to 99? And from 1 to 199?

#
Notice that among the numbers involved in the product, there are those ending in 5.

## Solution

The product of any sequence of numbers, among which there are numbers ending in 5, will end in either 0 (if there is at least one even number in the sequence) or 5 (if all numbers are odd). In both cases here, there are no even numbers, but there are numbers ending in 5, so the last digit in both products will be 5.

## Answer

## $5 ; 5$.