#### Chessboard v/s Rice story. Is it true?

Once upon a time in ancient India, a ruler was captivated by the intricate game of chess, a creation that had just unfolded. Filled with joy and admiration, the ruler sought to reward the genius behind this strategic game â€“ a man known for his wisdom and prowess in mathematics.

## First Read this table

Square | Value |
---|---|

1 | 2 |

2 | 4 |

3 | 8 |

4 | 16 |

5 | 32 |

6 | 64 |

7 | 128 |

8 | 256 |

9 | 512 |

10 | 1024 |

11 | 2048 |

12 | 4096 |

13 | 8192 |

14 | 16384 |

15 | 32768 |

16 | 65536 |

17 | 131072 |

18 | 262144 |

19 | 524288 |

20 | 1048576 |

21 | 2097152 |

22 | 4194304 |

23 | 8388608 |

24 | 16777216 |

25 | 33554432 |

26 | 67108864 |

27 | 134217728 |

28 | 268435456 |

29 | 536870912 |

30 | 1073741824 |

31 | 2147483648 |

32 | 4294967296 |

33 | 8589934592 |

34 | 17179869184 |

35 | 34359738368 |

36 | 68719476736 |

37 | 137438953472 |

38 | 274877906944 |

39 | 549755813888 |

40 | 1099511627776 |

41 | 2199023255552 |

42 | 4398046511104 |

43 | 8796093022208 |

44 | 17592186044416 |

45 | 35184372088832 |

46 | 70368744177664 |

47 | 140737488355328 |

48 | 281474976710656 |

49 | 562949953421312 |

50 | 1125899906842624 |

51 | 2251799813685248 |

52 | 4503599627370496 |

53 | 9007199254740992 |

54 | 18014398509481984 |

55 | 36028797018963968 |

56 | 72057594037927936 |

57 | 144115188075855872 |

58 | 288230376151711744 |

59 | 576460752303423488 |

60 | 1152921504606846976 |

61 | 2305843009213693952 |

62 | 4611686018427387904 |

63 | 9223372036854775808 |

64 | 18446744073709551616 |

## In 10 Multiples

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|

2 * 10^1 | 4 * 10^1 | 8 * 10^1 | 1.6 * 10^2 | 3.2 * 10^2 | 6.4 * 10^2 | 1.28 * 10^3 | 2.56 * 10^3 |

5.12 * 10^3 | 1.02 * 10^4 | 2.05 * 10^4 | 4.10 * 10^4 | 8.19 * 10^4 | 1.64 * 10^5 | 3.28 * 10^5 | 6.56 * 10^5 |

1.31 * 10^6 | 2.62 * 10^6 | 5.25 * 10^6 | 1.05 * 10^7 | 2.10 * 10^7 | 4.19 * 10^7 | 8.39 * 10^7 | 1.68 * 10^8 |

3.36 * 10^8 | 6.72 * 10^8 | 1.34 * 10^9 | 2.68 * 10^9 | 5.37 * 10^9 | 1.07 * 10^10 | 2.15 * 10^10 | 4.29 * 10^10 |

8.59 * 10^10 | 1.72 * 10^11 | 3.44 * 10^11 | 6.89 * 10^11 | 1.38 * 10^12 | 2.75 * 10^12 | 5.51 * 10^12 | 1.10 * 10^13 |

2.20 * 10^13 | 4.39 * 10^13 | 8.79 * 10^13 | 1.76 * 10^14 | 3.52 * 10^14 | 7.05 * 10^14 | 1.41 * 10^15 | 2.82 * 10^15 |

5.65 * 10^15 | 1.13 * 10^16 | 2.26 * 10^16 | 4.53 * 10^16 | 9.07 * 10^16 | 1.81 * 10^17 | 3.62 * 10^17 | 7.25 * 10^17 |

1.45 * 10^18 | 2.90 * 10^18 | 5.81 * 10^18 | 1.16 * 10^19 | 2.32 * 10^19 | 4.65 * 10^19 | 9.31 * 10^19 | 1.86 * 10^20 |

Once upon a time in ancient India, a ruler was captivated by the intricate game of chess, a creation that had just unfolded. Filled with joy and admiration, the ruler sought to reward the genius behind this strategic game â€“ a man known for his wisdom and prowess in mathematics.

This ingenious individual, the creator of chess, approached the ruler with a seemingly modest request. He humbly asked for just one grain of rice to be placed on the first square of the chessboard on the first day, doubling that amount on the second square the next day, and continuing this pattern until all 64 squares were filled.

The ruler, intrigued and considering it a simple and economical request, readily agreed. Little did he know that this seemingly straightforward task would unfold into a mathematical marvel, revealing the astonishing power of exponential growth.

The initial grains of rice on the first few squares seemed inconsequential:

- Square 1: 1 grain
- Square 2: 2 grains
- Square 3: 4 grains
- …and so on.

However, as the doubling continued, the numbers quickly escalated beyond the ruler’s anticipation. By the **10th square**, there were already 512 grains â€“ still manageable. Yet, the pace of growth became apparent:

**Square 20**: 524,288 grains**Square 32**: 2,147,483,648 grains

It was on day 36 that the true impact hit â€“ a staggering 34,359,738,368 grains of rice added. The second half of the chessboard brought exponential growth to a shocking climax:

**Square 64**: 18446744073709551616 grains

If stacked, this mountain of rice would supposedly reach the summit of Mount Everest.

The wise man, far from being a fool, had orchestrated a demonstration of the “unbearable quickness of doubling.” The story of the chessboard rice serves as a metaphor for the rapid and impactful nature of exponential growth, a phenomenon businesses often encounter, especially in the second half of their strategic journey. At square 32, the tipping point is reached, where growth becomes not just significant but potentially chaotic and unsustainable. The tale of the chessboard rice reminds us of the profound consequences that can arise from the relentless doubling of even the most modest beginnings.

If we use the number **1 BILLION** from the last square (square 64) of the chessboard rice story as the capacity of each bag, we can calculate how many bags would be needed to contain **18,446,744,073,709,551,615** rice grains Number of bags=Grains per bag/Total grainsâ€‹Number of bags=18,446,744,073,709,551,6151,000,000,000 Number of bags=1,000,000,00018,446,744,073,709,551,615â€‹ Let’s calculate this: Number of bagsâ‰ˆ18,446,744,073.71Number of bagsâ‰ˆ18,446,744,073.71

If we express the result in scientific notation (10^), it would be:

[ \text{Number of bags} \approx 1.84467440737 \times 10^{10} ]So, it would take approximately 1.84467440737 x 10^10 bags to contain 1 billion rice grains if each bag can hold 1 billion grains. Therefore, in scientific notation, the answer is approximately (1.844 \times 10^{10}) bags.

So, it would take approximately 18,446,744,073.71 bags to contain 1 billion rice grains if each bag can hold 1 billion grains. Since we can’t have a fraction of a bag, we would need at least 18,446,744,074 bags.

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