Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

Find The Next Number in this series.
1, 2, 6, 42, 1806 ?

A girl was sitting in her hotel room when she heard a knock on the door. She opened the door and found that a man was standing outside.
The man said, "Oh! I am really sorry, I thought this was my room."
He then walked through the corridor to the elevator. The girl did not know the man. She closed her door and called security asking them to apprehend the man.
What made her suspicious of that man? He might have been genuinely mistaken.

I have branches, but no fruit, trunk or leaves. What am I?

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?

I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?

How many times do a clock's hands overlap in a day ?

Begin with a word, five letters to my name,
Remove the first and last but I am the same
Take out my middle and still, I remain.
What word am I?

In the image below, can you find the value of an angle(y)

Distances from you to certain cities are written below.

BERLIN 200 miles

PARIS 300 miles

ROME 400 milesAMSTERDAM 300 miles

CARDIFF ??? miles

How far should it be to Cardiff ?