Can you find the least possible number such that

If the number is divided by 3, it gives the remainder of 1;
If the number is divided by 4, it gives the remainder of 2;
If the number is divided by 5, it gives the remainder of 3;
If the number is divided by 6, it gives the remainder of 4.

What will be the best approach to finding all the prime numbers less than 75 that leave an odd reminder when we divide them with 5?

A father's child, a mother's child, yet no one's son.

Who am I?

One evening there was a murder in the home of a married couple, their son and daughter. One of these four people murdered one of the others. One of the members of the family witnessed the crime.

The other one helped the murderer.

These are the things we know for sure:

1. The witness and the one who helped the murderer were not of the same sex.

2. The oldest person and the witness were not of the same sex.

3. The youngest person and the victim were not of the same sex.

4. The one who helped the murderer was older than the victim.

5. The father was the oldest member of the family.

6. The murderer was not the youngest member of the family.

Who was the murderer?

Which digit occurred maximum times between the number 1 and 1000?

Only one color, but not one size,
Stuck at the bottom, yet easily flies.
Present in sun, but not in rain,
Doing no harm, and feeling no pain.
What is it?

John went to meet his friend Jacob, but when he was about to reach the main gate, John notices that Jacob had a mighty dog who was fastened to the tree. The chain is long enough that it allows the dog to reach the main gate.

How can the John reach the main gate?

It is a nine-letter word.
The exact opposite of the phrase "friendly and outgoing"
It contains the word "over".
It starts will a vowel.

What is it?

French Police inspects a room where there are no windows, no doors, no tables and is almost empty expect there is just a puddle of water. They found a dead man who obviously hung herself from the ceiling, but they are not able to figure out how this had happened.

John and Jacob entered the crime scene and easily able to solve the case.

How did the man die?

Find the next number in the series.
1 10 24 43 67 ?