In which direction should the missing arrow point?

Count the number of triangles in the picture below:

Sweet & very intelligent katty has 8 puppets(Jane Bird Barbie Angel Colleen Nora Lass Missy).
All puppets are of different size. She arrange all puppets to face towards the guest and tell the guess the following clues :

* Jane has three puppets bigger on its left side
* Bird has two puppets smaller on its left side
* Barbie has one puppet bigger on its right side
* Angel has two puppets smaller on its right side
* Colleen has one puppet bigger on its left side
* Nora has one puppet smaller on its left side
* Lass has four puppets bigger on its right side
* Missy has three puppets smaller on its right side

Also some puppets are inside the bigger puppets.

Assuming you are the guest , can you tell the katty how the puppets are arranged ?

Find the missing letter in the last circle logically in the given below picture.

Can you find a number that lies one third of the distance between 1/3 and 2/3?

You are given four results as below:
1111 = F
2222 = E
3333 = T
Then, can you find out how to code 4444?

You are in a room that has three switches and a closed door. The switches control three light bulbs on the other side of the door. Once you open the door, you may never touch the switches again. How can you definitively tell which switch is connected to each of the light bulbs?

One day Jenifer meets the Lion and the Tiger in the Forest of Forgetfulness. She knows that the Lion lies on Mondays, Tuesdays, and Wednesdays, and tells the truth on the other days of the week. The Tiger, on the other hand, lies on Thursdays, Fridays, and Saturdays, but tells the truth on the other days of the week. Now they make the following statements to Jenifer:

Lion: Yesterday was one of my lying days.

Tiger: Yesterday was one of my lying days too.

What day is it?

You walk into a room that contains a match, a kerosene lamp, a candle and a fireplace. What would you light first?

What 8 letter word can have a letter taken away and it still makes a word. Take another letter away and it still makes a word. Keep on doing that until you have one letter left. What is the word?