FIGURES THAT PUZZLE

Taranaki Daily News, Volume LI, Issue 92, 7 April 1908, Page 4

FIGURES THAT PUZZLE

"You cannot count a trillion." This was stilted iu ;i journal years ago. Many tried it. and all gave up before counting very long. Suppose von counted without slopping at the rale of two hundred every minute of the Jay anj night, lion Ion;: would it take': Vou eouhl count, 12.0(111 an hour: l'KS.oiiii in a day; ](>5,1!):2,(iU(l in a year of ;i(w'/, days. Since a billion is a thousand million, it is a simple matter to see thai it would take nearly ten ycarto reach that sum: and since a trillion is a thousand billion, it does not require a jjivat stretch of the imagination to mc that we could never reach thai annum! unless we had in the neighbourhood of len thousand years to devote to the task. A woman of social ambitions once remarked to an acquaintance, that she had eighteen intimate friends whom .she wished to have to dinner, but as he:, (able seated only eight she could only have six guests at a.* time. It wa's siiggc.-tcd that she invite them in rotation, changing the guests until each had been to dinner with all of th,. others. At I h<' lirst (tinner she announced her plan, and one of I In- gue-ls asked if 4 IV had counted the number of dinners she would have to give before she had made ihe complete rotation. When he learned that sh c thought twenty or thirty dinners would answer, he 'laughed, took a pencil from his pocket, ami after figuring a few minutes told her it would require l.S.olit dinner parties to finish her plan. At the rate of three, hundred each year this would require nearly sixtytwo years. The plan was abandoned.' He then suggested that »he. see how many ways she could spat the eight people round the table, and she was ready to try that as well until told that it was possible to arrange 40,:)2O settings without having any two alike. Suppose six horses ai'e entered in a race, If ,ome one should oiler to bet that you eouhl not tell the exact order in which (he six horses would cross the tape, yon would probably not care to lake the bet unless you were given goo.l odds, say fifty to one, or seveiity-fi\o to one. Many would be willing to bet under -uch condilons; but their chances I lo win would be exceedingly small. Any one of the horses might b ( , lirst; any one of the other live might lie second'; of the other four any one luiglil be lliird; there would Ik-'three choices for fourth place, two for lifth. and one for sixth. Now. since the same posibililics would remain, no mailer how we started, it is easy to -e,. how th,. total number of arrangements must be (i x 5 x -I x II x 2 x I. or 72(1. so that the bettor has exactly one chance iu 7211 of winning, provided he knows absolutely notliiii" about the hors,... If he takes odds of I"" to I. In. is almost certain to lose, for even at (his figure lie is really the one who has given the odds 72 to 1.