Originally Posted by TheSeeker

Fill in the missing number in the series.
3,10,7,8,--,12,9,16.

The missing number is 5

Here is how i found out

There are two sequences interwined

one is a sequence of even numbers and another one is a sequence of odd numbers

Consider the odd numbers and take three numbers at a time
the lowest number is 3 and the first set of 3 odd numbers would be 3,5 and 7.
Write them in the order of 1st, third and second ie (o1,o3,o2) this will give 3,7 and 5.
Next set would be 9,13 and 11 and so on and so forth

Now consider the even number. each set has three numbers in the increasing order
The lowest numbers so far here is 8. Suppose the first set consists of (a1,a2,a3) then rewrite them by (a2,a1,a3). So a set (8,10,12) will become (10,8,12) followed by (16,14,18) and so on and so forth.

Now combine these two sequences odd one first and in between any two odd numbers insert the even numbers and the series would unravel

3,10,7,8,5,12,9,16,13,14,11,18,15,22,19,20,17,24....