【Question 17】  
From $1,2, \cdots, 100$, if you arbitrarily take out 40 odd numbers, the possible unit digit of their product is $\qquad$ -
【Analysis and Solution】
Number Theory, Remainder.
(1) If the 40 odd numbers taken out contain "odd numbers with a units digit of 5"; $5 \times$ odd number has a units digit of 5;
the units digit of the product is 5.
(2) If the 40 odd numbers taken out do not contain "odd numbers with a units digit of 5"; then we need to take all the odd numbers with units digits of $1, 3, 7, 9$ from $1 \sim 100$; $1 \times 3 \times 7 \times 9$ has a units digit of 9;
$9^{1}$ has a units digit of $9, 9^{2}$ has a units digit of $1, 10 \div 2=5, 9^{10}$ has a units digit of 1; the units digit of the product is 1.
In summary, the units digit of the product could be 1 or 5.