Solution:

Sucre : 1 cupcake
T-Bag : 2 cupcakes
Burrows: 3 cupcakes
Scofield : 5 cupcakes

Explanation :
It's obvious if the prisoner has eaten 5 or more cupcakes than he will not ask this question "did you had more cupcakes than me?" as it will make him the person who had eaten maximum cupcakes.
A) Sucre : Must not have eater 5 cupcakes, therefore he has eaten anywhere between 1-4 cupcakes.

B) T-bag : Since sucre asked him the question T-bag knows sucre have eaten between 1 - 4 cupcakes, and therefore he must have eaten 2 to 4 cupcakes(it can't be 1 else he will reply answer as "No".)

C) Burrows : Replied with the answer as "I don't know and based on logic B) he knows T-bag must have eaten at least 2 and he replied no which implies that he must be eaten 3 or 4.

D) Scofield replied he know all, which indicates he must have eaten 5.
Therefore cupcake division is as below:
Sucre : 1
T-Bag : 2
Burrows: 3
Scofield : 5

Solution:

As shown in the picture below.
Cut 1 : Cut the cake across the diameter.
Cut 2 : Cut horizontally and you will get 4 equal pieces of cake
Cut 3 : Cut horizontally from other side and you will get 8 equal pieces of cake

Solution:

In the attached picture, you can see that the formation allows 2 castles to be protected by the walls. Congrats!

Solution:

1/3

Explanation
Assuming T1 is the Toy for brother1, T2 is the toy for brother2 and T3 is the toy for brother3.

Following are the possible cases for toys distribution:

Boy1 Boy2 Boy3
T1 T2 T3
T1 T3 T2
T2 T1 T3
T2 T3 T1 .... (A)
T3 T1 T2 .... (B)
T3 T2 T1

In both steps (A) & (B), no one gets the correct toy.
Therefore probability that none brother can get the own toy is 2/6 = 1/3

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:

Mr. Orange is wearing a Green shirt.
Mr. Pink is wearing an Orange shirt.
Mr. Green is wearing a Pink shirt.

One should notice that the person wearing Green shirt agreed to Mr. Pink's statement which implies that Mr. Pink is not wearing Green. Obviously, he cannot be wearing a Pink shirt which is why he must be wearing an Orange shirt.

Now, we can easily deduce that the Green shirt is being worn by Mr. Orange and the Pink shirt by Mr. Green since they must be wearing a color different than their names.

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:

A) Fill 5 ml gallon ( 5mlGallon - 5, 3mlGallon - 0)
B) Transfer to 3 ml gallon (5mlGallon - 2, 3mlGallon - 3)
C) Empty 3 ml gallon ( 5mlGallon - 2, 3mlGallon - 0)
D) Transfer 2 ml from 5 ml gallon to 3 ml gallon (5mlGallon - 0, 3mlGallon - 2)
E) Fill 5 ml gallon(5mlGallon - 5, 3mlGallon - 2)
F) Transfer 1 ml from 5 ml gallon to 3 ml gallons(5mlGallon - 4, 3mlGallon - 3)

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.