There is a bag which have 21 blue balls and 23 red balls. You also have 22 red balls outside the bag. Randomly remove two balls from the bag. * If they are of different colors, put the blue one back in the bag. * If they are the same colour, take them out and put a red ball back in the bag. Repeat this until only one ball remains in the bag. What is the color of the sole ball left in the bag ?
In the picture, you can see a chess board. On the top left position, the K marks a knight. Now, can you move the knight in a manner that after 63 moves, the knight has been placed at all the squares exactly once excluding the starting square?
What is the four-digit number in which the first digit is one-third the second, the third is the sum of the first two, and the last is three times the second?