I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?

Count the number of squares in the picture below.

Analyze and find the missing item in the sequence:
16, 06, 68, 88, __, 98

There is an exact a week gap between Christmas and New Year. Hence, It is obvious that the new year that comes right after Christmas comes on the same day of the week.

A Strange thing happened in the Year 1777. Christmas occurs on Wednesday and New Year on Monday. How is that possible?

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

The two towns are exactly 100 km apart. John leaves City A driving at 30 km/hr and Jacob leaves City B half an hour later driving at 60 km/hr. Who will be closer to City A when they meet?

Tell me the Hindi name of a Vegetable which if we remove 1st word will become a precious Stone and by removing the last word it will become a sweet eatable.

As we know that white starts the game of chess. Can you find the scenario shown in the picture below is possible when all the white pieces are at the original place while the black pawn is not as in the below picture?

Mr Black, Mr Gray, and Mr White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr Black, who hits his shot 1/3 of the time, gets to shoot first. Mr Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr Black, where should you shoot first for the highest chance of survival?

What does the below mathematical rebus mean?