Solution:

73

Explanation:
It's a very famous puzzle known as "Josephus Problem Puzzle". It can be solved in various ways but the trick to solve this problem is illustrated below.

Binay number of 100 is: 1100100
complement pf 100 is 0011011, whose decimal equivalent is 27.
The desired answer will be 100 - 27 = 73

Solution:

You just need to check $150 bag.

Explanation:
Note: All bags labels are incorrect.
Case 1: If it contains $100 bill, then
A) Current bag contains $200 bills
B) $100 bag contains $150 bills
C) $200 bag contains $100 bills

Case 2: If it contains $50 bill, then
A) Current bag contains $100 bills.
B) $100 bag contains $200 bills
C) $200 bag contains $150 bills

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:

63.984375

Explanation:
This question is hypothetical because you cannot transact in fractions in bank account. The following is the solution:

Year Amount Interest and Deduction
Start 63.984375
Y1 End 62.968750 63.984375 * 2 - 65
Y2 End 60.937500 62.96875* 2 - 65
Y3 End 56.875000 60.9375 * 2 - 65
Y4 End 48.750000 56.875 * 2 - 65
Y5 End 32.500000 48.75 * 2 - 65
Y6 End 0.000000 32.5 * 2 - 65 = 0

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.