A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

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?

I want to fill my bucket using both cold and hot water.
I have two taps for both cold and hot water. The hot water tap fills the bucket in exact 6 hours and the cold water tap fills the bucket in exact 4 hours.
I turn both of them simultaneously but I forgot to turn off another tap which removes the water out of the bucket. This tap can empty the bucket in 12 hours.

How Long will it take to fill the bucket?

Can you find out the remainder when 3^300 is divided by 5?

Name one eight-letter word with 'kst' in the middle, 'in' the beginning, 'and' at the end.?

You are an expert on paranormal activity and have been hired to locate a spirit haunting an old resort hotel. Strong signs indicate that the spirit lies behind one of four doors. The inscriptions on each door read as follows:

Door A: It's behind B or C
Door B: Its behind A or D
Door C: It's in here
Door D: It's not in here

Your psychic powers have told you three of the inscriptions are false, and one is true. Behind which door will you find the spirit?

In a boat, the father of a sailor's son is sitting with the son of the sailor. However, the sailor is not present on the boat.

Can this even be possible?

Place a mathematical symbol between the numerals 5 and 9 in such a way that the resulting number is greater than 5 but smaller than 9.

2, 3, 5, 9, 17, _ What is the next number in the sequence?

Look at me. I can bring a smile to your face, A tear to your eye, Or even a thought to your mind. But, I can't be seen. What am I?