I am eight letters long - "12345678"
My 1234 is an atmospheric condition.
My 34567 supports a plant.
My 4567 is too appropriate.
My 45 is a friendly thank-you.
My 678 is a man's name.

What word am I?

It is always ahead of me yet I can never see it. What is it?

Can you find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours.

What number does the below three word/phrase identify and why?
1. Deck
2. Year
3. Singing in the Rain

A mother is 21 years older than her child. In exactly 6 years from now, the mother will be exactly 5 times as old as the child.
Where's the father?

A time long back, there lived a king who ruled the great kingdom of Trojan House. As a part of the renovation of the kingdom to meet future security needs, he asked his chief architect to lay down a new play in a manner that all of his 10 castles are connected through five straight walls and each wall must connect four castles together. He also asked the architect that at least one of his castles should be protected with walls. The architect could not come up with any solution that served all of King's choices, but he suggested the best plan that you can see in the picture below. Can you find a better solution to serve the king's demand?

Can you count the number of triangles in the given figure?

John killed hundreds of people mercilessly and yet the police were not able to put her behind the bars. Why?

What does this mathematical rebus means ?

A 52% bias toss for head using the 51% tail bias coin was done to obtain a fair result.

Can you find how bias is the floor in this case?