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

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?

A bag contains 64 balls of eight different colours. There are eight of each colour (including red). What is the least number you would have to pick, without looking, to be sure of selecting 3 red balls?

Six glasses are in a row. The first three are filled with milk and the last three are empty. By moving only one glass, can you arrange them so that the full and the empty glasses alternate?

Alpha is Beta's sister.

Gamma is a Beta mother.

Delta is Gamma's father.

Tango is Delta's mother.

Then,

How is Alpha related to Delta?

If I put in one canary per cage, I have one bird too many. If I put in two canaries per cage, I have one cage too many. How many cages and canaries do I have?

Find the next number in the series?
2, 12, 36, 80, 150, 252, 392, _ ?

A dying old man wants to divide his entire land between his only two sons. Since his only wish is to treat them as equal as both of them have been too good to him, he wants to divide his land equally between them. The problem is that the land is significantly irregular in shape and thus there is no choice of cutting them into two equal halves.

Can you help him divide the land in a manner that both of his sons will be happy?

Two brothers were watching a horror film on video late one night. One brother dozed off and dreamed that he was being chased by the crazy man from the movie, who was trying to kill him. In the dream, he hid in a cupboard. There was no sound except his heart pounding, and he had no idea where his crazed captor was. He was terrified! At that moment, the video finished, and his brother put his hand on the shoulder of his sleeping sibling to wake him. The shock at that tense moment was enough that the sleeping brother suffered a massive heart attack and died instantly. True or false?

As shown in the image, the nine Dogs are square fenced. By constructing just two square fences can you make sure that two Dogs cannot meet each other without crossing the fence?