Q. What is the unit digit in the multiplication of 1 × 3 × 5 × 7 × 9 × … × 999?

Explanation : 

1. We want the units digit of the product
P = 1 × 3 × 5 × 7 × 9 × … × 999.

2. Note there are (999 + 1)/2 = 500 odd numbers from 1 to 999.

3. Look at the factors’ last digits; they cycle every five terms:
1, 3, 5, 7, 9, 1, 3, 5, 7, 9, …

4. Compute the product of one cycle modulo 10:
1 × 3 = 3
3 × 5 = 15 → last digit 5
5 × 7 = 35 → last digit 5
5 × 9 = 45 → last digit 5
⇒ Product of any block of five consecutive odd numbers ends in 5.

5. Since there are 500 odd numbers, that is 100 such blocks.
So P ≡ 5¹⁰⁰ (mod 10).
But 5^k always ends in 5 for any k ≥ 1.

6. Therefore, the units digit of P is 5.