Solution:

252

Explanation:
A unique pattern has been made into use in this series.
All numbers are (n^3 + n^2) where n is 1, 2, 3 and so on.

In first number, n = 1
1^3 + 1^2 = 1 + 1 = 2

In second number, n = 2
2^3 + 2^2 = 8 + 4 = 12

In third number, n = 3
3^3 + 3^2 = 27 + 9 = 36

In fourth number, n = 4
4^3 + 4^2 = 64 + 16 = 80

In fifth number, n = 5
5^3 + 5^2 = 125 + 25 = 150

Similarly for the sixth number, n = 6
6^3 + 6^2 = 216 + 36 = 252.

Solution:

Yes, some people are going get really tiny pieces but you were allowed for that right. Also, there is another way of doing it. Can you think of it?

Solution:

The answer is very simple. All she had to do is take the fifteen cards from the top and reverse them. This would make another pile out of that and there will be two piles - one of 15 cards and one of 37 cards. Also both of them will have the same number of inverted cards.

Just think about it and if the mathematical explanation will help you understand better, here it is.
Assume that there were p inverted cards initially in the top 15 cards. Then the remaining 37 cards will hold 15-p inverted cards.
Now when she reverses the 15 cards on the top, the number of inverted cards will become 15-p and thus the number of inverted cards in both of the piles will become same.

Solution:

It was only a trick

I borrowed my parents (Pound 50 + Pound 50 = Pound 100).
I bought the book for Pound 97 and i had Pound 3 change.
So, the money that i borrowed and bought the book are Pound 100 (borrowing money)
and the change Pound 3 also the borrowing money the book is Pound 97
Total: Pound 97 + Pound 3(the change) = Pound 100
The money that i used to buy the book all i borrowed.
Pound 97 is the borrowing money, change: Pound 3 also the borrowing money. Pound 97 + Pound 3 = Pound 100

Solution:

The person on 73rd number will survive.

Explanation:
Till the number is the power of 2, the last person to survive will be the one who started it. But since the number here is not the power of 2, we will take the greatest power of 2 that is less than the number which is 64.
100 - 64 = 36
36 people are killed as 2, 4, 6, ..., 72. Thus the sword will now be given to the 73rd person. Now he is the first person to start in the remaining 64 people. Thus he will be the one to survive.

Solution:

Difference 1
Toy plane direction is different.

Difference 2
On the clock, number 1 & 2 is missing.

Difference 3
The colors of lamp's light is changed.

Difference 4
The ribbon on the gift is missing.

Difference 5
Duck is added in the gift section.

Solution:

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

Solution:

Numbers of the first cube:
1, 2, 4, 0, 5 and 6.

Numbers on the second cube:
3, 1, 2, 7, 8 and 0.

Now you can pick any date and you will be able to show it using these cubes. Remember that you can always use 6 as 9 by inverting it.

This problem has another solution and we leave it for you to deduce.

Solution:

The node can be connected as shown.

Solution:

Hockey Stick $49.50 & ball $0.50

Solution:

The stranger said that he thought the room was his. If so, he must have had the keys to the room and thus he must not have knocked.