Solution:

7 Trips

Explanation:
Send 2+5+9 = 16
Bring back 9
Send 3+4+9 = 16
Bring back 9
Send 1+7+8 = 16
Bring back 1
Send 1+6+9 = 16

Solution:

Pour 3 lumps on cup-1 and cup-3 and 4lumps on cup4 and place them as shown in the picture.

Explanation:
Now,
Cup-1 got three sugar lumps
Cup-3 got three sugar lumps
Cup-2 got three seven lumps (3 of cup-1 and 4 of its own)

Solution:

Federer serves first

Explanation:
The one who serves first can serve 5 and other will serve four.

== Option A ==
If Federer serve 4 and Nadal serve 5
Then five service breaks and Federer winning 6:3 not possible.

== Option B ==
Federer serve 5 and Nadal serve 4
There are five service breaks and score is Federer 6 - Nadal 3
i.e
On Federer serve, Federer wins 3 and lost 2
On Nadal serve, Federer wins 3 and lost 1

Solution:

The code is 645
Explanation :
A) From Clues 1st and 2nd we know that one 9 is not in the code
B) From Clue 2nd we know that 9 3 and 8 are part of code
C) From Clue 3rd we know that 4 and 6 are part of code
D) From Clue 5th we know that 1 and 2 are not part of the code as we know 6 is part of the code and just 1 of 3 numbers is part of code.
E) From Clue 4th we know that 5 is also in the code as 8 and 1 are not part of code.

So the code is: 645

Solution:

The chocolates in the boxes will be as follows:
Box 1 = 1
Box 2 = 2
Box 3 = 4
Box 4 = 8
Box 5 = 16
Box 6 = 32
Box 7 = 64
Box 8 = 128
Box 9 = 256

Here we have taken a geometric progression to facilitate any number of chocolates demanded. In the last box, we will place the number of chocolates left:

Box 10 = 489

If you try now, you will be able to do what is asked.

Solution:

It's simple puzzle
Distance = speed * time
= 2meter/seconds * 2 * 50 * 60
= 14400 meteres
= 14.4 kms

My thoughts -
This puzzle reminds us of life when we are stuck at a difficult situation and stop losing hope but if try hard it can be actually a simple problem.

Solution:

833 pears

Explanation:
Step one: First you want to make 3 trips of 1,000 pears 333 kilometers. You will be left with 2,001 pears and 667 kilometers to go.

Step two: Next, you want to take 2 trips of 1,000 pears 500 kilometers. You will be left with 1,000 pears and 167 kilometers to go (you have to leave a pear behind).

Step three: Finally, you travel the last 167 kilometers with one load of 1,000 pears and are left with 833 pears in Cherryville

Solution:

f the last elf is taking some time to answer the question then it shall mean that the elf's before him are all wearing distinct coloured hats. However sufficient time shall be given to the last elf to give the answer.
If he views the similar coloured hats in front of him , he shall quickly tell the answer

Solution:

The probability of two numbers being relatively prime is 60%. Thus if you keep playing the bet, you will hypothetically make 20 cents on every play.

Thus, you should accept the bet.

Solution:

The integer with the special property is -1.

To test the property, let us subtract any digit from it, let's say 5.

-1 - 5 = -6

The succeeding digit of 5 is 6.

When (-6) is divided by 6, it is completely divided.

For all other numbers as well, this stands true.