TherewasonceavictimofoverwhelmingnumberscalledKingShirhamofIndia,who,accordingtotheoldlegend,wantedtorewardhisgrandPrimeMinisterSissaforinventingandpresentingtohimthegameofchess.
Thedesireofthecleverministerseemedverymodest.
“Majesty,”hesaidkneelinginfrontoftheking,“givemeagrainofwheattoputonthefirstsquareofthischessboard,andtwograinstoputonthesecondsquare,andfourgrainstoputonthethird.
Andso,ohKing,doublingthenumberforeachsucceedingsquare,givemeenoughgrainstocoverall64squareoftheboard.”
“Youdonotaskformuch,ohmyfaithfulservant,”exclaimedtheking,secretlyenjoyingthethoughtthathisliberalproposalofagifttotheinventorwouldnotcosthimmuchofhistreasure.
“Yourwishwillcertainlybegranted.”
Andheorderedabagofwheattobebroughttothethrone.
Butwhenthecountingbegan,itwasfoundthatthebagwasemptiedbeforethetwentiethsquarewasaccountedfor.
Morebagsofwheatwerebroughtbeforethekingbutthenumberofgrainsneededforeachsucceedingsquare
increasedsorapidlythatitsoonbecameclearthatwithallthecropofIndianthekingcouldnotfulfillhispromisetoSissa.
Todosowouldhaverequired18,446,744,073,709,551,615grains!
Assumingthatabushelofwheatcontainsabout5milliongrains,onewouldneedsome4×1012bushelstosatisfythedemandofSissa.
Sincetheworldproductionofwheataveragesabout2×109bushelsayear,theamountrequestedbytheministerwasthatoftheworld'swheatproductionfortheperiodofsometwothousandyears!
ThusKingShirhamfoundhimselfdeepindebttohisministerandhadeithertofacetheincessantflowofthelatter'sdemands,ortocuthisheadoff.
Wesuspectthathechosethelatteralternative.