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

All of you like to eat me. I am a five-lettered word. Remove the first two and I turn into an infamous animal. Remove just the first and I become a heinous crime. Remove the first and the last and you can groove on me.

Can you guess who am I?

Evil warlock dislikes dwarfs and therefore he selects four of them and buries them. The dwarfs are buried in the ground and they are in such a way that except for their heads, their body is inside the ground. The dwarfs cannot move their body and they can view only forward. They are all buried in a line, and amongst the four, one of the dwarfs is separated by a wall. All the dwarfs are in the same direction. The last dwarfs can see two heads of friends in the front and a wall. In the last second dwarf can see one head of his friend and a wall. The second dwarf can see only the wall. The dwarf can see nothing.
Warlock comprehends the situation and tells the dwarfs that he has placed hats on their heads. There are two blue hats and two red ones. In all four dwarfs, one of them has to say what colour hat he is wearing. If the dwarf says the correct colour of the hat, they will be left free. If the answer is wrong, then they will be dug inside the ground till the very end.

What will be the answer by the dwarf and how will they answer?

In the addition below, all digits have been replaced by letters. Equal letters represent equal digits and different letters represent different digits.
ABCABA
BBDCAA
ABEABB
ABDBAA
------- +
AAFGBDH
What does the complete addition look like in digits?

Can you solve this amazing hard number series problem?
7, 8, 10, 12, 16, 18 ?

While handling a project, the landscaper is asked by the owner of the mansion that he wants four trees in front of his mansion that are exactly equidistant from each other.

How will he do it?

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 ?

Thomas has missed an excessive number of days of school, so he must meet with Principal Davis. Mr. Davis asks him "Why on Earth have you missed so many days?" Thomas replies "There just isn't enough time for school. I need 8 hours of sleep a day, which adds up to about 122 days a year. Weekends off is 104 days a year. Summer vacation is about 60 days. If I spend about an hour on each meal, that's 3 hours a day or 45 days a year. I need at least 2 hours of exercise and relaxation time each day to stay physically and mentally fit, adding another 30 days. Add all of that up and you get about 361 days. That only leaves 4 days for school." The principal knows Thomas is full of it, but can't figure out why. Where is Thomas going wrong?

There are seven sisters in a house in a village where there is no electricity or any gadget.

Sister-1: Reading Novel
Sister-2: Cooking
Sister-3: Playing Chess
Sister-4: Playing Sudoku
Sister-5: Washing clothes
Sister-6: Gardening

what is Sister-7 doing ?

John is a strange liar.

He lies on six days of the week, but on the seventh day, he always tells the truth.

He made the following statements on three successive days:

Day 1: "I lie on Monday and Tuesday."
Day 2: "Today, it"s Thursday, Saturday, or Sunday."
Day 3: "I lie on Wednesday and Friday."

On which day does John tell the truth?