The history of chess

The earliest versions of the game originated in India, about 1,500 years ago.

From India, the game spread to Persia, where learning to play chess was part of the education of kings and nobles. When the Arabs conquered Persia, they took up the game and when the Muslims expanded their empire, they spread the game to Southern Europe. In Europe, chess evolved into its current form in the 15th century.

In the second half of the 19th century, modern chess tournament play began, and the first world Chess Championship was held in 1886. The 20th century saw great leaps forward in chess theory and the establishment of the World Chess Federation (FIDE).

Developments in the 21st century include use of computers for analysis. In the 1970s the first programmed chess games became available. Online gaming appeared in the mid 1990's.

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D O T H E M A T H - O U R P O P U L A T I O N G R O W T H R A T E I S U N S U S T A I N A B L E

Grains of wheat on a Chessboard - Part 1

Legend has it that the game of chess was invented by a mathematician who worked for a king. The king was very pleased and wanted to reward him. So, the mathematician said: “My needs are modest. Please take my new chess board and, on the first square place one grain of wheat. On the next square place 2 grains of wheat. On the next square, double that to 4 grains of wheat. On the next, 8 grains, then 16 grains on the next, doubling each time. Just keep doubling for every square and that will be an adequate payment.”

The king thought, “This foolish man. I was ready to give him a real reward, and all he asked for is a few grains of wheat.”

Let’s take a closer look at this.

Grains of wheat on a chessboard

Square	Grains on the Square	Total Grains on the Whole Board
1	1	1
2	2	3 (or 22 minus 1)
3	4  (this is 2 x 2, or 22)	7 (or 23 minus 1)
4	8  (this is 2 x 2 x 2, or 23)	15 (or 24 minus 1)
5	16  (this is 2 x 2 x 2 x 2, or 24)	31 (or 25 minus 1)
6	32  (2 x 2 x 2 x 2 x 2, or 25)	63 (or 26 minus 1)
7	64  (2 x 2 x 2 x 2 x 2 x 2, or 26)	127 (or 27 minus 1)
8	128  (27)	255 (or 28 minus 1)
9	256  (28)	511 (or 29 minus 1)
10	512   (29)	1,023 (or 210 minus 1)
11	1024   (210)	2,047 (or 211 minus 1)
12	2048   (211)	4,095 (or 212 minus 1)
skip ahead one row 20	skip ahead one row 1,067,008  (219)	skip ahead one row 2,134,105 ) (or 220 minus 1)
skip ahead to the last square 64	skip ahead to the last square 263	skip ahead to the last square 264 minus 1

How many grains on a square?

On the 4th square, there are 8 grains of wheat. That’s three 2s multiplied together or 2 x2 x2. In other words, the number of 2s in the calculation is one less than the number of the square. We write it as 2³.

On the 8th square, there are 128 grains of wheat. That’s seven 2s multiplied together or 2 x2 x2 x2 x2 x2 x2. In other words, the number of 2s in the calculation is one less than the number of the square. We write it as 2⁷.

On the 20th square there are over one million grains of wheat! That’s nineteen 2s multiplied together or 2 x2 x2 x2 x2 x2 x2 x2 x2 x2 x2 x2 x2 x2 x2 x2 x2 x2 x2. We write it as 2¹⁹.

So, on the last square, which is the 64th square, we find the answer by multiplying 63 2s together. You don't need to do this now, just keep reading.
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