Easy #1

Notice that $5$ is in the product. Also, notice that the last digit of any number multiplied by $5$ if I the number is odd, and $0$ if the number is even. But since the product $1 \times 3 \times \ldots\times 999$ does not have a factor of $2$ , hence the number is odd, and therefore ends in $5$ .

Any odd number multiply by 5 ends with 5. And multiply all odd numbers from 1 to 999 is an odd number.

What matters is that there's at least one multiplicand that's unit digit is $5$ . Hence the unit's digit of the product is $5$ .

Hey @Victor Loh , thanks for doing this. I will be taking it very shortly.