Solution:

101/125

Explanation:
This is an extremely tricky question. You have to find the probability where all of them have same number in mind. But if you try to do that, you will have to do a lot of calculations and utilize your brain plenty much. However, the trick to do this question is something opposite. We are not implying that you won’t get answer by directly calculating the probabilities, but it will take much time.

However, if you just go on calculating the negative probabilities, then you can simply subtract it from 1 to find the positive probability. Let us begin the operations and not confuse you further more.

Let us take two friends in the beginning. The probability that Adam and Bella don’t have the same number in their respective mind will be 4/5.

Now let us include Christopher in the scene. The probability that Christopher don’t have a digit same as either Adam or Bella will be 3/5.

Let us now include Drew as well. The probability that she does not have any number in mind which is same as either Adam or Bella or Christopher will be 2/5.

Now the combined probability that none of them has the same number in mind will be:
4/5 * 3/5 * 2/5 = 24/125

Now the probability that they have same number in mind will be:
1 – 24/125 = 101/125

Solution:

Four

three placed flat on the table in a triangle(touching each other) and put the fourth one on top of them in the middle.

Solution:

Mercury

Solution:

2 cakes

At each toll bridge you are required to give half of your cakes, and you receive one back. Which leaves you with 2 cakes after every bridge.

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.