SOLUTION: Please fill in next 2 digits in the series 10,3, 9, 5, 8, 4

Look at the ODD terms only:

10, __, 9, __, 8, __,

I would suppose the next ODD term would be 7, wouldn't you?"
So the odd terms would go:

10, __, 9, __, 8, __, 7, __, 6, __, 5, __, 4, __, 3, __, 2, __, 1

Look at the EVEN terms only:

__, 3, __, 5, __, 4,

I would assume that is going 3,5,4,6,8,7,9,11,10 

So it's

even terms: 10,    9,    8,    7,    6,    5,    4,    3,     2,     1 

Odd terms:      3,    5,    4,    6,    8,    7,    9,    11,    10,   

together:   10, 3, 9, 5, 8, 4, 7, 6, 6, 8, 5, 7, 4, 9, 3, 11, 2, 10, 1

Edwin