document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=53325>Question 53325</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4) 	CLASSIC PROBLEM - A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Brown came out and gratefully thanked the traveling salesman for saving his daughter’s life.  Mr. Brown insisted on giving the man an award for his heroism. \r<BR>\n" );
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document.write( "So, the salesman said, “If you insist, I do not want much. Get your checkerboard and place one penny on the first square. Then place two pennies on the next square. Then place four pennies on the third square. Continue this until all 64 squares are covered with pennies.” As he’d been saving pennies for over 25 years, Mr. Brown did not consider this much of an award, but soon realized he made a miscalculation on the amount of money involved.<BR>\n" );
document.write( "a) 	How much money expressed in dollars would Mr. Brown have to put on the 32nd square?<BR>\n" );
document.write( "Answer:	<BR>\n" );
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document.write( "b) 	How much money expressed in dollars would the traveling salesman receive in total if the checkerboard only had 32 squares?<BR>\n" );
document.write( "Answer:	<BR>\n" );
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document.write( "c) 	Calculate the amount of money necessary to fill the whole checkerboard (64 squares). How money expressed in dollars would the farmer need to give the salesman?<BR>\n" );
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document.write( "Show work in this space	\r<BR>\n" );
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document.write( "You have a question like this but it doesnt answer all 3 questions. Please help.<BR>\n" );
document.write( "THANK YOU </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #35587 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=35587\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A traveling salesman<BR>\n" );
document.write( "(selling shoes) stops at a farm in the Midwest. Before<BR>\n" );
document.write( "he could knock on the door, he noticed an old truck on<BR>\n" );
document.write( "fire. He rushed over and pulled a young lady out of<BR>\n" );
document.write( "the flaming truck. Farmer Brown came out and<BR>\n" );
document.write( "gratefully thanked the traveling salesman for saving<BR>\n" );
document.write( "hsi daughter's life. Mr. Brown insisted on giving the<BR>\n" );
document.write( "man an award for his heroism.<BR>\n" );
document.write( "So, the salesman said, \"If you insist, I don not want<BR>\n" );
document.write( "much. Get your checkerboard and place one penny on the<BR>\n" );
document.write( "first square. Then place two pennies on the next<BR>\n" );
document.write( "square. Then place four pennies on the third square.<BR>\n" );
document.write( "Continue this until all 64 squares are covered with<BR>\n" );
document.write( "pennies.\" As he'd been saving pennies for over 25<BR>\n" );
document.write( "years, Mr Brown did not consider this much of an<BR>\n" );
document.write( "award, but soon realized he mad a miscalculation on<BR>\n" );
document.write( "the amount of money involved.<BR>\n" );
document.write( "a)How much money would Mr. Brown have to put on the<BR>\n" );
document.write( "32nd square? Show work<BR>\n" );
document.write( "b)How much would the traveling salesman receive if the<BR>\n" );
document.write( "checkerboard only had 32 squares?show work<BR>\n" );
document.write( "C) Calculate the amount of money necessary to fill the<BR>\n" );
document.write( "whole checkerboard (64 squares). How much money would<BR>\n" );
document.write( "the farmer need to give the salesman? Show work.<BR>\n" );
document.write( "1 solutions<BR>\n" );
document.write( "Answer 21618 by venugopalramana(1719) About Me  on<BR>\n" );
document.write( "2006-04-29 05:55:27 (Show Source):<BR>\n" );
document.write( "YOU CAN USE IT TO<BR>\n" );
document.write( "GOOD EFFECT TO PUT ACROSS A PROPOSAL TO A FRIEND ...<BR>\n" );
document.write( "YOU PROMISS HIM A 100,000..POUNDS EVERY DAY FOR 30<BR>\n" );
document.write( "DAYS.LET HIM GIVE YOU IN RETURN JUST A PENNY ON THE<BR>\n" );
document.write( "FIRST DAY,2 PENNIES ON THE SECOND DAY ,4 PENNIES ON<BR>\n" );
document.write( "THE THIRD DAY,......ETC FOR 30 DAYS ..AS IN YOUR<BR>\n" );
document.write( "PROBLEM... I PRESUME HE WILL<BR>\n" );
document.write( "LAP ON THE PROPOSAL AND I CAN ASSURE YOU THAT YOU WONT<BR>\n" );
document.write( "REGRET THE PROPOSAL!!!!<BR>\n" );
document.write( "OK NOW LET US GET BACK TO YOUR PROBLEM AS WELL AS MY<BR>\n" );
document.write( "SUGGESTION ,WHICH IS JUST A PART OF IT .I AM GIVING<BR>\n" );
document.write( "BELOW THE MONEY TO BE PAID ON THIS BASIS FOR 30 AND 64<BR>\n" );
document.write( "DAYS ,ROUNDED OFF TO POUNDS OR MILLION POUNDS AT THE<BR>\n" );
document.write( "LATER DAYS.<BR>\n" );
document.write( "DAY.....MONEY TO BE PAID........MONEY TO BE PAID BY<BR>\n" );
document.write( "YOUR FRIEND TO YOU IN<BR>\n" );
document.write( "............TO YOUR FRIEND.....<BR>\n" );
document.write( "CENTS...POUNDS...MILLION POUNDS<BR>\n" );
document.write( "................POUNDS<BR>\n" );
document.write( "1 100000 1 0 0<BR>\n" );
document.write( "2 100000 2 0 0<BR>\n" );
document.write( "3 100000 4 0 0<BR>\n" );
document.write( "4 100000 8 0 0<BR>\n" );
document.write( "5 100000 16 0 0<BR>\n" );
document.write( "6 100000 32 0 0<BR>\n" );
document.write( "7 100000 64 1 0<BR>\n" );
document.write( "8 100000 128 1 0<BR>\n" );
document.write( "9 100000 256 3 0<BR>\n" );
document.write( "10 100000 512 5 0<BR>\n" );
document.write( "11 100000 1024 10 0<BR>\n" );
document.write( "12 100000 2048 20 0<BR>\n" );
document.write( "13 100000 4096 41 0<BR>\n" );
document.write( "14 100000 8192 82 0<BR>\n" );
document.write( "15 100000 16384 164 0<BR>\n" );
document.write( "16 100000 32768 328 0<BR>\n" );
document.write( "17 100000 65536 655 0<BR>\n" );
document.write( "18 100000 131072 1311 0<BR>\n" );
document.write( "19 100000 262144 2621 0<BR>\n" );
document.write( "20 100000 524288 5243 0<BR>\n" );
document.write( "21 100000 1048576 10486 0<BR>\n" );
document.write( "22 100000 2097152 20972 0<BR>\n" );
document.write( "23 100000 4194304 41943 0<BR>\n" );
document.write( "24 100000 8388608 83886 0<BR>\n" );
document.write( "25 100000 16777216 167772 0<BR>\n" );
document.write( "26 100000 33554432 335544 0<BR>\n" );
document.write( "27 100000 67108864 671089 1<BR>\n" );
document.write( "28 100000 134217728 1342177 1<BR>\n" );
document.write( "29 100000 268435456 2684355 3<BR>\n" );
document.write( "30 100000 536870912 5368709 5<BR>\n" );
document.write( "31 100000 1073741824 10737418 11<BR>\n" );
document.write( "32 100000 2147483648 21474836 21<BR>\n" );
document.write( "33 100000 4294967296 42949673 43<BR>\n" );
document.write( "34 100000 8589934592 85899346 86<BR>\n" );
document.write( "35 100000 17179869184 171798692 172<BR>\n" );
document.write( "36 100000 34359738368 343597384 344<BR>\n" );
document.write( "37 100000 68719476736 687194767 687<BR>\n" );
document.write( "38 100000 1.37439E+11 1374389535 1374<BR>\n" );
document.write( "39 100000 2.74878E+11 2748779069 2749<BR>\n" );
document.write( "40 100000 5.49756E+11 5497558139 5498<BR>\n" );
document.write( "41 100000 1.09951E+12 10995116278 10995<BR>\n" );
document.write( "42 100000 2.19902E+12 21990232556 21990<BR>\n" );
document.write( "43 100000 4.39805E+12 43980465111 43980<BR>\n" );
document.write( "44 100000 8.79609E+12 87960930222 87961<BR>\n" );
document.write( "45 100000 1.75922E+13 175921860444 175922<BR>\n" );
document.write( "46 100000 3.51844E+13 351843720888 351844<BR>\n" );
document.write( "47 100000 7.03687E+13 703687441777 703687<BR>\n" );
document.write( "48 100000 1.40737E+14 1407374883553 1407375<BR>\n" );
document.write( "49 100000 2.81475E+14 2814749767107 2814750<BR>\n" );
document.write( "50 100000 5.6295E+14 5629499534213 5629500<BR>\n" );
document.write( "51 100000 1.1259E+15 11258999068426 11258999<BR>\n" );
document.write( "52 100000 2.2518E+15 22517998136853 22517998<BR>\n" );
document.write( "53 100000 4.5036E+15 45035996273705 45035996<BR>\n" );
document.write( "54 100000 9.0072E+15 90071992547410 90071993<BR>\n" );
document.write( "55 100000 1.80144E+16 180143985094820 180143985<BR>\n" );
document.write( "56 100000 3.60288E+16 360287970189640 360287970<BR>\n" );
document.write( "57 100000 7.20576E+16 720575940379279 720575940<BR>\n" );
document.write( "58 100000 1.44115E+17 1441151880758560 1441151881<BR>\n" );
document.write( "59 100000 2.8823E+17 2882303761517120 2882303762<BR>\n" );
document.write( "60 100000 5.76461E+17 5764607523034230 5764607523<BR>\n" );
document.write( "61 100000 1.15292E+18 11529215046068500 11529215046<BR>\n" );
document.write( "62 100000 2.30584E+18 23058430092136900 23058430092<BR>\n" );
document.write( "63 100000 4.61169E+18 46116860184273900 46116860184<BR>\n" );
document.write( "64 100000 9.22337E+18 92233720368547800 92233720369<BR>\n" );
document.write( "30<BR>\n" );
document.write( "DAY..3000000.........1073741823......10737418.....................11<BR>\n" );
document.write( "TOTAL<BR>\n" );
document.write( "64<BR>\n" );
document.write( "DAY..6400000.........1.84467E+19.....184467440737095000......184467440737<BR>\n" );
document.write( "TOTAL<BR>\n" );
document.write( "YOUR GAIN IN 30 DAYS = 8 MILLION POUNDS..GOT IT BUT<BR>\n" );
document.write( "ONLY BE CAREFULL THAT YOUR FRIEND WONT RUN OUT OF YOU<BR>\n" );
document.write( "ON THE 25 TH. DAY.!!!<BR>\n" );
document.write( "YOUR GAIN IN 30 DAYS = 184467440731 MILLION POUNDS<BR>\n" );
document.write( "NOW COMING TO THE MATHS PART OF THIS ,THIS SEQUENCE<BR>\n" );
document.write( "WHERE EACH NUMBER BEARS A CONSTANT RATIO TO ITS<BR>\n" );
document.write( "PREDECESSOR IS CALLED GEOMETRIC PROGRESSION..HERE YOU<BR>\n" );
document.write( "FIND EACH NUMBER IS OBTAINED FROM THE PREVIOUS ONE BY<BR>\n" );
document.write( "MULTIPLYING WITH 2 , CALLED COMMON RATIO.<BR>\n" );
document.write( "THE LAST NUMBER ON NTH. DAY AND SUM OF SUCH SERIES OF<BR>\n" );
document.write( "NUMBERS UPTO THE N TH.DAY IS GIVEN BY THE FOLLOWING<BR>\n" );
document.write( "FORMULAE...<BR>\n" );
document.write( "N TH. NUMBER = FIRST NUMBER *(C0MM0N RATIO<BR>\n" );
document.write( ")^(N-1)=A*(R)^(N-1)=(2)^(N-1) IN THIS CASE.<BR>\n" );
document.write( "SUM UP TO N TH.NUMBER =A*{((R)^N -<BR>\n" );
document.write( "1))/(R-1)}={(2)^N-1}IN THIS CASE<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );