I am quite hot but become too cold if you remove the first two letters. What am I?

The more you take me, the more you leave me behind.
Who Am I?

Considering the below equation:

V + II - VI = 10
IV - X + VIII = 20
IV - VII + VI = 30

Then, I + II + III = ?

If 1+9+8=1, what is 2+8+9?

Can it be possible to build a house that has all its four walls facing towards the South?

Make a sentence consisting of three words that have the whole alphabet.

As a whole I am both
safe and secure.

Behead me and I become
a place of meeting.

Behead me again and I am
the partner of ready.

Restore me, and I become
the domain of beasts.

What am I?

A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?

Given that

(78)^9 = 6
And (69)^4 = 11

Can you find out

(99)^2 =?

(Note: This is Logical, not Mathematical)

1 dollar = 100 cent
= 10 cent x 10 cent
= 1/10 dollar x 1/10 dollar
= 1/100 dollar
= 1 cent

=> 1 dollar = 1 cent

solve this tricky problem?