Problem Statement:If a chessboard were to have wheat (or Rice) placed upon each square such that one grain were placedon the first square, two on the second, four on the third, and so on (doubling the number ofgrains on each subsequent square), how many grains of wheat would be on the chessboard atthe finish?

Square No:

1st 12nd 23rd 44th 85th 166th 327th 648th 1289th 25610th 51211th 102412th 204813th 409614th 819215th 1638416th 3276817th 6553618th 13107219th 26214420th 52428821st 104857622nd 209715223rd 419430424th 838860825th 1677721626th 3355443227th 6710886428th 13421772829th 26843545630th 536870912

Calculation Using Simple Running Product and then Cummulative Summation

Number of Grains in each Square ∑_(𝑛=0)^63▒〖 (2)〗^𝑛 =((1−2^((63+1) )))/((1−2))=((1−2^64))/((−1))=2^64−1="(1.84467"×

〖 10〗 ^19 " )"

31st 107374182432nd 214748364833rd 429496729634th 858993459235th 1717986918436th 3435973836837th 6871947673638th 13743895347239th 274877906944 Total40th 549755813888 Total41st 109951162777642nd 219902325555243rd 439804651110444th 879609302220845th 1759218604441646th 3518437208883247th 7036874417766448th 14073748835532849th 28147497671065650th 56294995342131251st 112589990684262452nd 225179981368524853rd 450359962737049654th 9.00719925474099E+01555th 1.8014398509482E+01656th 3.6028797018964E+01657th 7.20575940379279E+01658th 1.44115188075856E+01759th 2.88230376151712E+01760th 5.76460752303424E+01761st 1.15292150460685E+01862nd 2.30584300921369E+01863rd 4.61168601842739E+01864th 9.22337203685478E+018

Total 1.84467440737096E+019

Grains 1.84467440737096E+19Masha 2.30584300921369E+18Tolla 1.92153584101141E+17

Grams 1.60127986750951E+16Kilograms 1.60127986750951E+13

Manns 4.00319966877377E+11

Tonnes 1.60127986750951E+10

Above Calculations are based on the local weightage units widely used in Sub-Continent

If a chessboard were to have wheat (or Rice) placed upon each square such that one grain were placedon the first square, two on the second, four on the third, and so on (doubling the number ofgrains on each subsequent square), how many grains of wheat would be on the chessboard at

Calculation Using Finite Sum Formula

Grains

Picture illustrating a chess board with no. of grains on each square

Here letters 'K, M, T, G, P' reperesetn standared prefixes Kilo, Mega, Giga, Exa, Peta etc.

∑_(𝑛=0)^63▒〖 (2)〗^𝑛 =((1−2^((63+1) )))/((1−2))=((1−2^64))/((−1))=2^64−1="(1.84467"×〖 10〗 ^19 " )"

Assuming 25 mg as the mass of one grain of rice as referred from

GRAINS 18,446,744,073,709,500,000 GrainsWEIGHT 461,168,602,000 Metric Tonnes1 METRIC TONNE has 40000000 grains1 KG has 39999.9999863597 grains1 GRAM has 39.9999999863597 grains1 TOLLA has 3.33333333219664 grains1 MASHA has 0.41666666652458 grains

Same results are obtained using MATLAB.FOR loop can be used.

http://web.archive.org/web/20060823025557/http://www.ricecrc.org/reader/tg_Size_and_Weight.htm

Above Calculations are based on the fact that 1 grain has a weight of 25 mg (milli gram)