Therewasonceavictimofoverwhelmingnumbers
calledKingShirhamofIndia,
who,accordingtotheoldlegend,
wantedtorewardhisgrandPrimeMinisterSissaforinventing
andpresentingtohimthegameofchess.
Thedesireofthecleverministerseemedverymodest.
“Majesty,”hesaidkneelinginfrontoftheking,
“givemeagrainofwheattoputonthefirstsquareofthischessboard,
andtwograinstoputonthesecondsquare,
andfourgrainstoputonthethird.
Andso,ohKing,doublingthenumberforeachsucceedingsquare,
givemeenoughgrainstocoverall64squareoftheboard.”
“Youdonotaskformuch,ohmyfaithfulservant,”
secretlyenjoyingthethought
thathisliberalproposalofagifttotheinventor
wouldnotcosthimmuchofhistreasure.
“Yourwishwillcertainlybegranted.”
Andheorderedabagofwheattobebroughttothethrone.
itwasfoundthatthebagwasemptied
beforethetwentiethsquarewasaccountedfor.
Morebagsofwheatwerebroughtbeforetheking
butthenumberofgrainsneededforeachsucceedingsquare
thatitsoonbecameclearthatwithallthecropofIndian
thekingcouldnotfulfillhispromisetoSissa.
Todosowouldhaverequired18,446,744,073,709,551,615grains!
Assumingthatabushelofwheatcontainsabout5milliongrains,
onewouldneedsome4×1012bushelstosatisfythedemandofSissa.
Sincetheworldproductionofwheataveragesabout2×109bushelsayear,
theamountrequestedbytheministerwasthatoftheworld’swheatproduction
fortheperiodofsometwothousandyears!
ThusKingShirhamfoundhimselfdeepindebttohisminister
andhadeithertofacetheincessantflowofthelatter’sdemands,
ortocuthisheadoff.
Wesuspectthathechosethelatteralternative.