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jmc

number theory senior

Problem

The double factorial, denoted by , returns the product of all of the odd integers that are less than or equal to . For example, . What is the units digit of ?
Solution
For any , we note that is the product of a set of odd integers and is thus odd. For , then is divisible by . Thus, the units digit of must be for . Hence, the units digit of the sum is units digit of the sum of , times. The units digit of is also . Now, we have to sum this with , yielding that the answer is .
Final answer
9