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

You have to put a letter on the following to make it a meaningful word. The only challenge is that you can't use 'E'.

S E Q U E N C _

What does man love more than life, and hate more than death or mortal strife; that which satisfied men want; the poor have, and the rich require; the miser spends, the spendthrift saves, and all men carry to their graves?

Luis Garavito killed Density x Volume.

Who is Luis Garavito ?

You are given 16 witch hats. The hats are divided in four different colours – red, blue, green and yellow. Every colour has been assigned to four hats. Now each of the hat will be glued with a label of an arithmetic sign – ‘+’, ‘-‘, ‘x’ or ‘/’. But you can label one sign only once on one colour. In such an arrangement, the hats can be uniquely defined by its colour and symbol.

Can you arrange all the 16 hats in a 4x4 grid in a fashion that no two rows and columns have a repetition of colour or sign?
We have arranged four hats in the below picture to assist you.

What question can you never answer yes to?

That attorney is my brother, testified the accountant.

But the attorney testified he didn't have a brother.

Who is lying?

Make eight squares by moving only two matchsticks.
Note- Square can be of different sizes.

A man is looking at a photograph of someone. His friend asks who it is. The man replies, “Brothers and sisters, I have none. But that man’s father is my father’s son.” Who was in the photograph?

There are 2 cops parked along a one-way street looking for traffic violations. They spot a taxi driver going in the wrong direction, yet they do nothing.

Why?