I am white when I am dirty, and black when I am clean. What am I?

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

Find out a multi-digit number that if multiplied by the number 9 or any of its multiplications products (i.e. 18, 27, 36, 45,..) will result in the multiplication factor repeated (n) number of times.

In the addition below, all digits have been replaced by letters. Equal letters represent equal digits and different letters represent different digits.
ABCABA
BBDCAA
ABEABB
ABDBAA
------- +
AAFGBDH
What does the complete addition look like in digits?

I cry without having a voice.
I fly without having wings.
I bite without having teeth.
I whisper without a mouth.

Who am I?

I taste better than I can smell. Who am I?

Spelt forwards I’m what you do every day, spelled backwards I’m something you hate. What am I?

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.

There were five men at church, and it started raining while they were outside. The four that ran still got wet, but the one that was still stayed completely dry. Why did he stay dry?

A bag contains 64 balls of eight different colours. There are eight of each colour (including red). What is the least number you would have to pick, without looking, to be sure of selecting 3 red balls?