The Legend of ChessBoard
Once upon a time, {come on! I had to start like that ;-)} there lived a king. He had acres and acres of land under his rule with bountiful crop year after year.
One day, a courtier gifted the king with a beautifully crafted hand-made chessboard. It was indeed one of its kind, and the king was very much impressed with the art work and detailing present in chessboard. So the king asked the courtier - what will he have in return? And the courtier requested rice grains in return to the tune of the rice that can be collected by placing one rice grain on the first square, two rice grains on the second square, four rice grains on the third square, so on and so forth until the sixty-fourth square of the chessboard.
The king laughed it out, and asked his men to immediately give the courtier his requested number of rice grains. But even after days of calculation and months assessment the king could not fulfil this simple request and finally gave up.
The king laughed it out, and asked his men to immediately give the courtier his requested number of rice grains. But even after days of calculation and months assessment the king could not fulfil this simple request and finally gave up.
So what was the quantity the courtier really requested? Let's deep dive with an excel sheet -
This is assuming that each rice grain's weight is 0.025 grams which is a decently accurate guesstimation. The courtier requested 461168601842739000.00 grams of rice. What's the big deal, it is a quantifiable unit after all. But here are some interesting facts when you try to get a perspective of that quantity -
| Square # | Rice Grains | Weigh (gm) | Sum@Sq# (gm) |
| 1 | 1 | 0.03 | |
| 2 | 2 | 0.05 | |
| 3 | 4 | 0.10 | |
| 4 | 8 | 0.20 | |
| 5 | 16 | 0.40 | |
| 6 | 32 | 0.80 | |
| 7 | 64 | 1.60 | |
| 8 | 128 | 3.20 | |
| 9 | 256 | 6.40 | |
| 10 | 512 | 12.80 | |
| 11 | 1024 | 25.60 | |
| 12 | 2048 | 51.20 | |
| 13 | 4096 | 102.40 | |
| 14 | 8192 | 204.80 | |
| 15 | 16384 | 409.60 | |
| 16 | 32768 | 819.20 | 1638.38 |
| 17 | 65536 | 1638.40 | |
| 18 | 131072 | 3276.80 | |
| 19 | 262144 | 6553.60 | |
| 20 | 524288 | 13107.20 | |
| 21 | 1048576 | 26214.40 | |
| 22 | 2097152 | 52428.80 | |
| 23 | 4194304 | 104857.60 | |
| 24 | 8388608 | 209715.20 | |
| 25 | 16777216 | 419430.40 | |
| 26 | 33554432 | 838860.80 | |
| 27 | 67108864 | 1677721.60 | |
| 28 | 134217728 | 3355443.20 | |
| 29 | 268435456 | 6710886.40 | |
| 30 | 536870912 | 13421772.80 | |
| 31 | 1073741824 | 26843545.60 | |
| 32 | 2147483648 | 53687091.20 | 107374182.38 |
| 33 | 4294967296 | 107374182.40 | |
| 34 | 8589934592 | 214748364.80 | |
| 35 | 17179869184 | 429496729.60 | |
| 36 | 34359738368 | 858993459.20 | |
| 37 | 68719476736 | 1717986918.40 | |
| 38 | 137438953472 | 3435973836.80 | |
| 39 | 274877906944 | 6871947673.60 | |
| 40 | 549755813888 | 13743895347.20 | |
| 41 | 1099511627776 | 27487790694.40 | |
| 42 | 2199023255552 | 54975581388.80 | |
| 43 | 4398046511104 | 109951162777.60 | |
| 44 | 8796093022208 | 219902325555.20 | |
| 45 | 17592186044416 | 439804651110.40 | |
| 46 | 35184372088832 | 879609302220.80 | |
| 47 | 70368744177664 | 1759218604441.60 | |
| 48 | 140737488355328 | 3518437208883.20 | 7036874417766.38 |
| 49 | 281474976710656 | 7036874417766.40 | |
| 50 | 562949953421312 | 14073748835532.80 | |
| 51 | 1125899906842620 | 28147497671065.60 | |
| 52 | 2251799813685250 | 56294995342131.20 | |
| 53 | 4503599627370500 | 112589990684262.00 | |
| 54 | 9007199254740990 | 225179981368525.00 | |
| 55 | 18014398509482000 | 450359962737050.00 | |
| 56 | 36028797018964000 | 900719925474099.00 | |
| 57 | 72057594037927900 | 1801439850948200.00 | |
| 58 | 144115188075856000 | 3602879701896400.00 | |
| 59 | 288230376151712000 | 7205759403792790.00 | |
| 60 | 576460752303424000 | 14411518807585600.00 | |
| 61 | 1152921504606850000 | 28823037615171200.00 | |
| 62 | 2305843009213690000 | 57646075230342400.00 | |
| 63 | 4611686018427390000 | 115292150460685000.00 | |
| 64 | 9223372036854780000 | 230584300921369000.00 | 461168601842739000.00 |
| Total | 18446744073709600000 | 461168601842739000.00 |
This is assuming that each rice grain's weight is 0.025 grams which is a decently accurate guesstimation. The courtier requested 461168601842739000.00 grams of rice. What's the big deal, it is a quantifiable unit after all. But here are some interesting facts when you try to get a perspective of that quantity -
- If you end up stacking this many number of rice grains, it will be the size of mount everest.
- If you end up weighing these many number of rice grain, it will be approximately 101 trillion pounds or 461 billion metric tons
- This requested rice quantity is around 1000 times more than the global rice production in 2010.
This also brings us to another interesting idea. It is known as Second Half of the ChessBoard. If you look closely, you will realize that the first half of the chessboard requires a total quantity of rice to be around 100,000 kgs. Good enough? Well, India's annual rice output is 1,200,000 times that amount. But, by the time you reach 64th square that quantity of rice is 1000 times the global rice production. Isn't it mind boggling, the numbers added by the second half of the chess board. This is where an exponentially growing factor begins to have a significant impact.
Hence, the bottomline! Compounding in investing works on two basic premises -
- The earnings have to be reinvested with the principal.
- The longer you wait, the more significant wealth you generate.
That is the power of compounding! Now, you know ...