Can you count the number of quadrilaterals in the picture below?

I know a 5-digit number having a property that With a 1 after it, it is three times as large as it would be with a one before it.

Guess the number?

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 ?

In a jungle where there are no street lights or any other artificial source of lights, I notice a black snake crossing the road.
How did I get sight of the snake?

Can you solve this picture maths equation?

_ _ _ IE _ _
_ _ _ IE _
_ _ IE _ _
_ _ IE _
_ _ _ _ IE

Like you see, some letters have gone missing from these words that contain the IE pair at some or the other place. The letters that will be used to fill the blanks are given below. Use them and form meaningful words. Can you do that?

A, C, D, F, H, K, L, M, N, N, O, R, R, S, S, S, T, T, Y and Y.

A chess tournament is taking place on knock-out terms (the one who loses the match is out of the game).
(a) If 10 matches are played in total, how many players participated?
(b) If 20 players took part in the tournament, how many matches were played?

What does this below rebus puzzle mean?

Rearrange the letters in "new door" to make one word.

Find the next number in the series below

21 32 54 87 131 ?