What seven-letter word has hundreds of letters in it?

Two old friends, Jack and Jill, meet after a long time, and discussing as:

Jack: Hey, how are you, man?

Bill: Not bad, got married and I have three kids now.

Jack: That's awesome. How old are they?

Bill: The product of their ages is 72 and the sum of their ages is the same as your birth date.

Jack: Cool..But I still don't know.

Bill: My eldest kid just started taking piano lessons.

Jack: Oh, now I get it.

How old are Bill's kids?

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

Why Wine Glass Stem is so long?

In the image given, you can find several triangles. Can you count them all?

Every words stands for unique digit that makes the arithmetic equation true

SEVEN + SEVEN + SIX = TWENTY.

What are the digits ?

Can you find a pattern and the missing number in the series given below?

100, 155, 258,? , 584, 819.

When you say goodbye, I am what you need to tie.
I come as a couple and go wherever you run.
Who am I?

What is the largest number you can write with just 3 digits?

I have a five and a three-gallon jar. Assuming there is an infinite supply of water, how can I measure one-gallon water?