# CHALLENGE

CHECKERBOARD MATH

Have you ever played the game of checkers?

It's played on a board that has squares on it that alternate between 2 colors, usually black and red. The squares are arranged into 8 rows and 8 columns.

Answer these questions regarding the checkerboard:

1) How many squares are on a checkerboard?

2) When played, each of 2 players each fills one color of 3 rows with checkers. (1 player has black, the other player has red.)

A) How many checkers are there?

B) How many empty squares are there?

C) What fraction of the squares is filled with red squares?

3) There is a story about an inventor who was promised by a king that he would be given 1 grain of rice on the first square, 4 on the third, 8 on the fourth, continuing to double the amount on each successive square.

A) How many grains of rice would be on the last square in the third row?

B) How many grains would be on the last square?

C) If each grain is 1/4 inches long (6mm), how many miles long (kilometers) would the grains be if placed end-to-end?

4) A domino exactly covers 2 squares.

A) How many dominoes will be needed to cover all the squares?

B) How many dominoes are needed to cover all the squares except 1 black and 1 red square?

C) How many dominoes are needed to cover all the squares except for 2 red squares?