The Chess Board and the Grain

Long long ago in an ancient land, there lived a very wise man who happenedto be the Vizier at the court of a great Sultan.

Months and years passed by and the great Sultan died, and his young prince replaced him. Being young, the prince lacked experience. He started spendingmore than what his father used to. The wise Vizier decided to teach the brashprince a lesson!

The prince set a contest and as a reward, decided to give the winner whateverhe wishes, boasting of his wealth, being under the illusion that his wealth isvirtually endless. The Vizier won, and asked the prince for the prize: a singlegrain of wheat and a chess board!

"What?! Just a grain of wheat! Are you insulting my wealth?" yelled the prince.
"No! Your majesty!" The Vizier explained. "You have to promise to double that grain of wheat until the chess board is full, so in the first day you give me one grain of wheat on the bottom right square of the chess board, on the second day you double it on the square next to it (giving me two grains), on the third, you double what is on the previous square (giving me four grains), and so on, until the Sixty Fourth square on the chess board."
"I would thought you being so smart", the young prince said. "You would ask for something more substantial. Anyway, if this is your wish I will grant you that."

And so, on the second day, the Vizier got 2 grains, on the third, he got 4 grains,and the young prince couldn't help himself making fun of the Vizier.

By the sixth day, the Vizier got 32 grains of wheat, at the end of the eighth daythe first row was over with a mere 128 grains. By the end of the sixteenth day, thesecond row was over with 32,768 grains.

Where was this leading to? Was it worth it for the Vizier.

By the end of the game (it was a mind game, wasn't it?) can you guess howmany grains the Vizier would get?

The prince could not provide enough grains to give the Vizier a chess board'sworth of grains. Why? Because there is not enough grains in the whole worldto give the Vizier the sum of 18,446,744,073,709,551,615 grains!

What? That much grains! I can't even spell that! It is 19 digits!

Yes my dear reader! This is the Power of Compounding. Take a look atthe table below, and get out your spreadsheet program and run the numberin it again!

Of course, you cannot expect that kind of return on your investments, butyou get the general idea of the Power of Compounding and how it can makeyou rich.

Sequence No. Running Total
1 1
2 3
3 7
4 15
5 31
6 63
7 127
8 255
9 511
10 1,023
11 2,047
12 4,095
13 8,191
14 16,383
15 32,767
16 65,535
17 131,071
18 262,143
19 524,287
20 1,048,575
21 2,097,151
22 4,194,303
23 8,388,607
24 16,777,215
25 33,554,431
26 67,108,863
27 134,217,727
28 268,435,455
29 536,870,911
30 1,073,741,823
31 2,147,483,647
32 4,294,967,295
33 8,589,934,591
34 17,179,869,183
35 34,359,738,367
36 68,719,476,735
37 137,438,953,471
38 274,877,906,943
39 549,755,813,887
40 1,099,511,627,775
41 2,199,023,255,551
42 4,398,046,511,103
43 8,796,093,022,207
44 17,592,186,044,415
45 35,184,372,088,831
46 70,368,744,177,663
47 140,737,488,355,327
48 281,474,976,710,655
49 562,949,953,421,311
50 1,125,899,906,842,623
51 2,251,799,813,685,247
52 4,503,599,627,370,495
53 9,007,199,254,740,991
54 18,014,398,509,481,983
55 36,028,797,018,963,967
56 72,057,594,037,927,935
57 144,115,188,075,855,871
58 288,230,376,151,711,743
59 576,460,752,303,423,487
60 1,152,921,504,606,846,975
61 2,305,843,009,213,693,951
62 4,611,686,018,427,387,903
63 9,223,372,036,854,775,807
64 18,446,744,073,709,551,615

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