FIGURES THAT PUZZLE.

Hawera & Normanby Star, Volume LIII, Issue LIII, 13 April 1908, Page 5

FIGURES THAT PUZZLE.

SOME PROBLEMS FOR THE ARITHMETICIAN.

*' You cannot count a trillion." This was stated in a journal years ago. Many . jtriedit,' but all , gave up before counting , very long. , ' Snpppse you 'counted without stopping at the rate of two hundred every , minute of the day and nighty how long. . would it tolce? Xou could count* 12,000 an hour; 288, ,000 in a d«y;,,i05,>92,p00 in a year of 365£ days,, . Since a* billion is a thousand - million, it is. a simple matter to- see that ' .it" would take .nearly .ten yeans to reach . that sum; and^ since' a trillion is a thousand billion, .it* does , not Bequir© a great ' stretch of the- imagination!. to ccV that wo .could never reacji that unless we had in, jfche i»igtbo)uihob<£ of ten thousand years to .devote to the .task. . A 'w,oman. of eocial,. ambitions once remarked to an acquaintance that she had' ■ eighteen intiin^e. friends. -w&om she wished., to have to dinner, but as her table ■Seated/ only^ight.shV .could have only sir guests' ,at/U) JGune,^ 'Jt^as 1 .suggested that jsjie in.^B tKe^a c jn.xgtaj; \.oix s changing the- , 'gW&ifiiWntir.eacß L'^j^-been to'diwner, but iWith'all of „ta,«; ' ", „At tic,. first /dinnejr. she announced her - plan, andone'of^tiit'gueste, asked if she had cplmted the - number of dinners she jwouid'haye to giyo before, she had) .mad© .' the ■ complete rotation*. When he learned -;' that .she '{{bought toyenity or dinners , laughed/ took a pencil ,- from his. pocket, «nttjifter figuring a few - minutes '.told her\ that it, would, -require ; dinner v parties"^ finish:' her plan. - At-' the. rate of^t^pee,.hu«daped each year j>his'wWld' requiije .nearly A sixty-two years. < The plan wafc,*biMWofie.d. '' ' j ; He. then . sugges&jd^ thaV she see how j. many wriys site could 1 «at the eight people / round the' table,' and she was ready to try that as weULnhtil ,~t»ld that' it was possible to'"arr>nge 50,320^eatings •wtt&o.ut having any'two.aKke, "Suppose, six horees are entered in a race.' If. some "one' should- offer to bet 1 that'.youi omiid:.. not tell tl» exact order in which tiie six, horses "would cross the toP 6 /* " you, would ~- probably" not care to • take the" bet amless'you were giv.en odds, ( fifty io one or' seventy-five to one. Many would be willing fo bet under i&uch conditions; but their' chances to win would bo exceedingly "smalls Anyone of the six , hordes might "be first; anyone of the other fivo might, be second; of the other > .four anyone, might be. third ; there would 'be", three' choices for, fourth place, two forfifth, anyone tor sirti. r . " Now, since the same, possibilities would rfemain,, no master "how we started, it is |asy to eed' that, the,' total .number of arrapgemenfis^inust" be. ,6xsx4x3x2xl or 720, so^tKat.lthe bitter h'asl exactly one chance irf 720 v oT .winaung,' "provided he knows absolutely ' nothing about the horses. If he takes odds of 100 to l/'he s s almost' certam to; lose, ior. ETOn at his figure he is',ireally the one "who- has civen the odds 7.2\tbl. .;- „."■-,;, «\ . One problem that seems almost beyond belief is based on , geometrical progression. It is related that a certain King, " pleased with some service of one of his subjects, told him that he would give him whatever he asked for a reward. The subject, a crafty man, ,told the King that he, woiild, be content with on© grain of wheat for t the first, square of the checker board} two for the B.eop.ji4, four, for the third, &n4 so on until the sixV--four squares had been covered. The King laughed and told him to count ou#the grains. - ' • Before the squares were half accounted for the Kin^ stopped him and asked if he^ would 1 be oontent with half of the kingdom instead, for he then saw what sort of a bargain he had 1 made. By continuing t&e muttipßcataon till Jn "fS, squares were accounted :: o c v f ° found that. oflO to{al &m^^ t agDn , «*aci called for 44,000,000,000,000 bushels «t wheat. .Continuing at ifie rate of two .hundred" a ."I"**!* woujd require one man j about 419,000 yeat'l $0 count the individual bushels. ~, ,