If eleven plus two equals one, what does nine plus five equal?

A chess tournament is taking place on knock-out terms (the one who loses the match is out of the game).
(a) If 10 matches are played in total, how many players participated?
(b) If 20 players took part in the tournament, how many matches were played?

The ages of a father and son add up to 66.
The father's age is the son's age reversed.
How old could they be?
(3 possible solutions).

As we know that white starts the game of chess. Can you find the scenario shown in the picture below is possible when all the white pieces are at the original place while the black pawn is not as in the below picture?

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?

I am a type of vehicle that has two wheels and is powered by humans. What am I?
Hint 1: You can ride me for exercise.
Hint 2: I am environment-friendly.

In a secret society, a buried chamber can be accessed only via a secret password. The password is seven characters long and comprises of just letters and numbers.

You find a code that can help you in cracking the password. The code says "You force heaven to be empty".

Can you deduce the password from that?

Forwards I am heavy, backward I am not. What am I?

Three people enter a room and have a green or blue hat placed on their heads. They cannot see their own hat but can see the other hats.
The colour of each hat is purely random. They could all be green, blue, or any combination of green and blue.
They need to guess their own hat colour by writing it on a piece of paper, or they can write 'pass'.
They cannot communicate with each other in any way once the game starts. But they can have a strategy meeting before the game.
If at least one of them guesses correctly they win $10,000 each, but if anyone guesses incorrectly they all get nothing.
What is the best strategy?

Find three whole, positive numbers that have the same answer when multiplied together as when added together.