I’m tall when I’m young, and I’m short when I’m old. What am I?

There is a basket full of hats. Three are white and two are black. Three men, Tom, Tim, and Jim, each take a hat out of the basket and put it on their heads without seeing the hat they selected or the hats the other men selected. The men arrange themselves so Tom can see Tim and Jim’s hats, Tim can see Jim’s hat, and Jim can’t see anyone’s hat. Tom is asked what color his hat is and he says he doesn’t know. Tim is asked the same question, and he also doesn’t know. Finally, Jim is asked the question, and he does know. What colour is his hat?

There are two insects on a tile. Insect X is sitting on one side of the tile (point A) and Insect Y is sitting opposite on the other side of the tile (point B). Now both of them decide to change their position and thus X starts crawling to point B and Y starts crawling to point A. When they meet and pass each other in between, X takes 20 seconds to reach B and Y takes just 5 seconds to reach A.

Can you calculate the total time each of the insects took to change their positions?

What is always in front of you but can’t be seen?

John bought 150 chocolates but he misplaced some of them. His Father asked him how many chocolates were misplaced.
He gave the following answer to him:
If you count in pairs, one remains
If you count in threes, two remain
If you count in fours, three remain
If you count in fives, four remain
If you count in sixes, five remain
If you count in sevens, no chocolate remains.

Can you analyze the statements and tell us how many chocolates were lost?

John is 45 years older than his son Jacob. If you find similarities between their ages, both of their ages contain prime numbers as the digits. Also, John's age is the reverse of Jacob's age.

Can you find their ages?

A family is trapped in a jungle. There is a bridge which can lead them to safety. But at one time, the bridge can only allow two people to pass through. Also, all of them are afraid of the dark and thus, they can't go alone.

Father takes 1 minute to cross, the mother takes 2 minutes, the son takes 4 and the daughter takes 5 minutes. While crossing the time taken will be according to the slower one. How can they all reach the other side in the minimum possible time?

You are a prisoner sentenced to death. The Emperor offers you a chance to live by playing a simple game. He gives you 50 black marbles, 50 white marbles, and 2 empty bowls. He then says, 'Divide these 100 marbles into these 2 bowls. You can divide them any way you like as long as you use all the marbles. Then I will blindfold you and mix the bowls around. You then can choose one bowl and remove ONE marble. If the marble is WHITE you will live, but if the marble is BLACK... you will die.'

How do you divide the marbles up so that you have the greatest probability of choosing a WHITE marble?

If,

20 % 5 = 24

21 % 7 = 33

42 % 6 = 67

Then;

66 % 6 = ?

What does this mean?

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