face up, face down

February 27, 2012

Posed by Punit Rathore:

A blind man is handed a deck of 52 cards and told that exactly 10 of these cards are facing up. How can he divide the cards into two piles, not necessarily of equal size, with each pile having the same number of cards facing up?

Solution posted in comment 1.

A set of tennis

February 14, 2012

Djokovic beat Nadal 6-3 in a set. There were a total of 5 broken games in that set. Who served first in that set? (A broken game is one in which the server loses the game)

calendar with 2 cubes

February 12, 2012

You are given 2 (regular, six sided) cubes and on each side of these cubes you are allowed to write any one single digit number. What numbers should each of these cubes have so that any day in the calendar (01,02, …, 31) can be represented using these  2 cubes?

Solution in comments.

shade and count

February 10, 2012

Each cell in the 8×8 square shown here is colored black or white with the following rules:

  1. each row has exactly same number (4) of white and black squares.
  2. each column has exactly the same number (4) of white and black squares.

Show that the sum of numbers in the 32 white squared cells is equal to the sum of numbers in the 32 black squared cells.

UPDATE: Hint in comment 1.