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 – 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 – 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 – 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 – 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 grains​Number of bags=18,446,744,073,709,551,6151,000,000,000 Number of bags=1,000,000,00018,446,744,073,709,551,615​ Let’s calculate this: Number of bags≈18,446,744,073.71Number of bags≈18,446,744,073.71

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.