So here is the algorithm I am trying to design...i'm not sure it will make any sense.

I have a sequence of n numbers(in ascending order). I have an another number 'x'. If i have 2 chances to compare x with a number greater than it but unlimited chances to compare with numbers lesser than it. Now I have to to find out the maximum possible value in the sequence that is less than x in the most efficient way. I know this looks a little contrived but the original question is different so I am looking for the direction I would need to go.

As an example..watch this..

I have a series from 1,2,3,4...............,19, 20.

Now I have a number x = 10.5

Now I have to find the maximum possible number "M" in the series such that M < x

The easiest way would be brute forcing ur way from the lowest possible number(they are in ascending order anyway.). As soon as the "less than comparison" fails, u have the solution. The worst case would 'n' comparisons. But we have two chances where we can fail the comparison. So a slightly better algorithm would be comparing the odd indexed numbers. So in the worst case scenario we have n/2 +1 comparisons which is better than the first.

Now finally...Is there a better way to approach this problem. Can some one point me in a better direction to solve the algorithm??