Russell ate several candies on halloween, and each day after halloween ate 6 fewer candies than the day before. his candies lasted exactly five days, and he ate 100 candies in total. how many did he eat on the third day?

Let a = the number of candies eaten on the first day.
Because the number of candies eaten decreases by 6 every day after, the number of candies eaten creates the arithmetic sequence
a, a-6, a-12, a-18, ..., 

After 5 days, the total candies eaten is 5a - 60.
Therefore
5a - 60 = 100
5a = 160
a = 32

On the third day, the number of candies eaten is
a - 12 = 32 - 12 = 20

20