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

There are three light switches outside a room. One of the switches is connected to a light bulb inside the room.
Each of the three switches can be either 'ON' or 'OFF'.

You are allowed to set each switch the way you want it and then enter the room(note: you can enter the room only once)

Your task is to then determine which switch controls the bulb?

There are a hundred statements.

First person says: At least one of the statements is false.

Second person says: At least two of the statements is false.

Third person says: At least three of the statements are false.

Fourth person says: At least four of the statements are false.

..

..

..

Hundredth person says: At least a hundred of the statements are false.

Analysing it, how many statements do you think are false and how many are true?

Find the next number in the series.
1 10 24 43 67 ?

If six children and two dogs were under an umbrella, how come none of them got wet?

I am not a bull but I have horns.
I am not an ass but I have a pack saddle.
Wherever I go, I leave silver behind me.

Who am I?

A network of 20 x 10 squares is given to you.

Can you calculate how many unique squares and rectangles can be formed combining two or more individual squares ?

What can run but never walk, have a mouth that never speaks, have a head that never weeps, and have a bed but never sleeps?

There is a five-letter word which has 3 consonants(all are same) and 2 different vowels.
Also, something wrong is associated with the word.

Can you name it?

What numbers should go on the bottom line?
3 6 9 15
8 2 10 12
11 8 19 27
19 10 29 39
? ? ? ?