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

• The expression is the product of all odd numbers from 1 to 999: 1 × 3 × 5 × 7 × ... × 999.

• The sequence includes the number 5, which is a factor in the multiplication.

• The sequence also includes the number 3, which is another factor in the multiplication.

• Since the product contains both 3 and 5 as factors, it contains 15 (3 × 5) as a factor.

• Any integer multiple of 5 that is not a multiple of 10 ends in 5, but more simply, any product containing a factor of 5 and an odd number (like 3) will result in a unit digit of 5 if the other factors do not introduce a factor of 2 to make it a multiple of 10. However, a simpler rule is that if a product contains a factor of 5 and at least one other odd number, the unit digit is 5. Actually, the most direct logic is: The product includes 5. The product also includes 3. 5 × 3 = 15, which ends in 5. Multiplying 15 by any other odd number (1, 7, 9, etc.) will always result in a number ending in 5 (e.g., 15×1=15, 15×7=105, 15×9=135). Therefore, the unit digit is 5.