There are six distinct colors and the cube has also 6 faces. that means it is not possible that two faces have the same color!! So if we number the colors 1-6 and the order of the faces will be: top, bottom, left, front, right, back and put the colors in this order than we have 6! =720 ways. But after we choose color 1 for the top there are 5 colors for the bottom. we are left with 4 colors that cab be arranged in 4! ways but each of them can be rotated 4 times to we actually have only 4!/4=6 unique ways. there are different ways for the top and bottom colors but the cube can be flipped on 3  different axis so we have 15*6/3=30 ways in total.

The clue for solving this riddle lies in the fact that: “land be divided such that each son is happy with his share“,  So it does not have to be equal at all, only close enough for equality!!. So it is very simple:  I suppose there is a map of the land. If so, take a the father (or any other person) can take a long enough item (a ruler) that covers that shape of the map and than starts slowly  moving it over the map. (lets say from left to right). The 1st son that says “STOP” will get the
area from the beginning until this point. This way we guarantee that “each son is happy with his share”. ( Neither of them will say “STOP” before he is sure that he does not get to much smaller than his brother).

8 Cases

28 shoes in a case => 28/2 =  14 pairs per case
112 pairs / 14 pairs (per case) = 8 Cases

I’ll give the car to my trustworthy friend, so he can take the woman to the hospital, and I will stay with the love of my life.

If you start the 5-min and 3-min timers together than after 3 minutes have passed you are left with 2 minutes until the 5-min timer stops. So start boiling the egg

He escapes at night through the 1st room

Lets go backwards. If there where only 3 seats and the 1st person did not take your seat than the 2nd person can choose between your seat or the 1st person seat so the probability is 1/2.

If there are 4 seats than there are 3 empty seats: yours, 1st person, and the person before the last. so the 2nd person has a probability of 1/3 that he chooses your seat, or 1st person seat, or the person before the last, So if he didn’t choose your seat we come back for the probability of 1/2 for the person before you and so on.

Since there is no friction at all’ than means that if I can create some movement once it begins it will not stop. (1st newtons rule). So If I’ll strongly throw away my  phone it will cause a movement to the opposite direction so that might get me out of there.