Solution:

David to play second

Explanation:
Let's suppose that David plays first and he picks 9. Then Albert will definitely pick 8. Now, David will have to pick 7 or Albert will pick 7 in his turn. But if David picks up 7, then he will score 16 that is beyond 15 and will lose. So one thing is for sure, no one will be willing to start with the highest digits.

Suppose David plays first and picks up 1, Albert will pick 2. Then David will pick 3 and Albert will pick 4. Now David will be forced to pick 9. The score is 6 to 13 and thus David will have no chance of winning.

If David Picks 9 after Albert has picked up 2, then Albert will pick 8 and the score will become 10 to 10. Thus David will pick 3 as picking 7 will send him past 15. Now Albert will pick 4 and David has nothing to pick for winning. Thus Albert wins.

Therefore, you should suggest David to play second.

Solution:

400

Explanation:
Begins with 15
2*15-1 => 29
2*29-2 => 56
2*56-4 => 108
2*108-8 => 208
2*208-16 => 400

Solution:

A green paint off-course :p

Solution:

At first, there were 2 apples on the tree. After the wind blew, one apple fell on the ground. So there where no apples on the tree and there were no apples on the ground.
*apples => more than one apple

Another solution(non tricky one)
The wind blew so hard that the apples fell of the tree and blew along the ground.

Solution:

1113213211


Explanation
1
one one => 11
two one => 21
one two , one one = > 1211
one one , one two , two one => 111221
three one , two two one one => 312211
one three, one one , two two, two one =>13112221

=>one one , one three, two one, three two, one one

Solution:

Put one red marble in one box and all other marbles in the 2nd box.

Probability :
50 + 24/49

Solution:

Belgium, Chile, Fiji, Egypt

Solution:

I filled a glass full of water and held it over my head for 20 minutes.

Solution:

Next in sequence is 13112221.

This series describes each number that came before it:
1 [One]
11 [One One]
21 [Two One(s)]
1211 [One Two and One One(s)]
111221 [One One, One Two, and Two One(s)]
312211 [Three One(s), Two Two(s), and One One]

The next number in the series is:
13112221 [One Three, One One, Two Two(s), Two One(s)]

Solution:

Jason Kumar

The number on the calendar was written in a hurry.Sherlock matched the written number with the months of the year.
So the B was an 8, thereby giving us 7-8-9-10-11: July, August, September, October, November.

Use the first letter of each month and it spells J-A-S-O-N.