Solution:

Let us denote the four people with A, B, C and D.
A takes 1 minute to cross, B takes 2, C takes 5 and D takes 10.

A and B cross first spending 2 minutes.
A comes back with torch taking 1 minute.
C and D cross taking 10 minutes.
B comes back with torch taking 2 minutes.
Finally, A and B cross the bridge taking 2 minutes.

2 + 1 + 10 + 2 + 2 = 17 minutes

Thus, this is the way they all managed to cross that bridge that night.

Solution:

The man asked the king that he wanted to die of old age.

Solution:

I + IX = X

The equation read from the other side becomes X = XI + I which is false.

Solution:

The wise man told them to switch the horses and then race. In this manner, both of them will be willing to race as fast as they can to prove that the other horse (his own horse) is slow.

Solution:

1 2 3 4 5 6 and 7 8 6

Since summation of numbers 1-9(1 2 3 4 5 6 7 8 9) is 45 , so its impossible to divide into two equal parts.
Since we cant flip over 6 to make it 9 but we can flip 9 to make it 6 and hence the solution

Solution:

To do this, he must be pushing the cork inside the bottle and then taking out the coin.

Solution:

NONE, holes are empty.

Solution:

17 min

The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? 10 + 1 + 7 + 1 + 2 = 21 minutes. Is that it? No. That would make this question too simple even as a warm up question.

Let's brainstorm a little further. To reduce the amount of time, we should find a way for 10 and 7 to go together. If they cross together, then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have 1 waiting on the other side to bring the torch back. Ahaa, we are getting closer. The fastest way to get 1 across and be back is to use 2 to usher 1 across. So let's put all this together.

1 and 2 go cross
2 comes back
7 and 10 go across
1 comes back
1 and 2 go across (done)

Total time = 2 + 2 + 10 + 1 + 2 = 17 minutes

Solution:

28 =>1+2+4+7+14

cannot be 1 (as number cannot be included)

Solution:

Align the toothpicks to form TEN. Use one toothpick for each of the lines.

Solution:

Fred Odea won.

Just look at the announcement lines. The first sentence in 'Ok now everybody!' If you take out just the first letter of every word, it will form 'ONE'. In the same manner the second sentence 'The winner of…..' will give form 'TWO' and the third sentence 'The Hardest Riddle Ever Event.' Will form THREE.

Thus the final sentence must form FOUR. There is only one candidate who can suffice with the first two letter and he is Fred Odea. The final sentence of the mastermind must be, 'Fred Odea: Ultimate Riddler!'