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Question 33999: 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 hsi daughter's life. Mr. Brown insisted on giving the man an award for his heroism.
So, the salesman said, "If you insist, I don 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 mad a miscalculation on the amount of money involved.
a)How much money would Mr. Brown have to put on the 32nd square? Show work
b)How much would the traveling salesman receive if the checkerboard only had 32 squares?show work
C) Calculate the amount of money necessary to fill the whole checkerboard (64 squares). How much money would the farmer need to give the salesman? Show work.
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! YOU CAN USE IT TO
GOOD EFFECT TO PUT ACROSS A PROPOSAL TO A FRIEND ...
YOU PROMISS HIM A 100,000..POUNDS EVERY DAY FOR 30
DAYS.LET HIM GIVE YOU IN RETURN JUST A PENNY ON THE
FIRST DAY,2 PENNIES ON THE SECOND DAY ,4 PENNIES ON
THE THIRD DAY,......ETC FOR 30 DAYS ..AS IN YOUR
PROBLEM... I PRESUME HE WILL
LAP ON THE PROPOSAL AND I CAN ASSURE YOU THAT YOU WONT
REGRET THE PROPOSAL!!!!
OK NOW LET US GET BACK TO YOUR PROBLEM AS WELL AS MY
SUGGESTION ,WHICH IS JUST A PART OF IT .I AM GIVING
BELOW THE MONEY TO BE PAID ON THIS BASIS FOR 30 AND 64
DAYS ,ROUNDED OFF TO POUNDS OR MILLION POUNDS AT THE
LATER DAYS.
DAY.....MONEY TO BE PAID........MONEY TO BE PAID BY
YOUR FRIEND TO YOU IN
............TO YOUR FRIEND.....
CENTS...POUNDS...MILLION POUNDS
................POUNDS
1 100000 1 0 0
2 100000 2 0 0
3 100000 4 0 0
4 100000 8 0 0
5 100000 16 0 0
6 100000 32 0 0
7 100000 64 1 0
8 100000 128 1 0
9 100000 256 3 0
10 100000 512 5 0
11 100000 1024 10 0
12 100000 2048 20 0
13 100000 4096 41 0
14 100000 8192 82 0
15 100000 16384 164 0
16 100000 32768 328 0
17 100000 65536 655 0
18 100000 131072 1311 0
19 100000 262144 2621 0
20 100000 524288 5243 0
21 100000 1048576 10486 0
22 100000 2097152 20972 0
23 100000 4194304 41943 0
24 100000 8388608 83886 0
25 100000 16777216 167772 0
26 100000 33554432 335544 0
27 100000 67108864 671089 1
28 100000 134217728 1342177 1
29 100000 268435456 2684355 3
30 100000 536870912 5368709 5
31 100000 1073741824 10737418 11
32 100000 2147483648 21474836 21
33 100000 4294967296 42949673 43
34 100000 8589934592 85899346 86
35 100000 17179869184 171798692 172
36 100000 34359738368 343597384 344
37 100000 68719476736 687194767 687
38 100000 1.37439E+11 1374389535 1374
39 100000 2.74878E+11 2748779069 2749
40 100000 5.49756E+11 5497558139 5498
41 100000 1.09951E+12 10995116278 10995
42 100000 2.19902E+12 21990232556 21990
43 100000 4.39805E+12 43980465111 43980
44 100000 8.79609E+12 87960930222 87961
45 100000 1.75922E+13 175921860444 175922
46 100000 3.51844E+13 351843720888 351844
47 100000 7.03687E+13 703687441777 703687
48 100000 1.40737E+14 1407374883553 1407375
49 100000 2.81475E+14 2814749767107 2814750
50 100000 5.6295E+14 5629499534213 5629500
51 100000 1.1259E+15 11258999068426 11258999
52 100000 2.2518E+15 22517998136853 22517998
53 100000 4.5036E+15 45035996273705 45035996
54 100000 9.0072E+15 90071992547410 90071993
55 100000 1.80144E+16 180143985094820 180143985
56 100000 3.60288E+16 360287970189640 360287970
57 100000 7.20576E+16 720575940379279 720575940
58 100000 1.44115E+17 1441151880758560 1441151881
59 100000 2.8823E+17 2882303761517120 2882303762
60 100000 5.76461E+17 5764607523034230 5764607523
61 100000 1.15292E+18 11529215046068500 11529215046
62 100000 2.30584E+18 23058430092136900 23058430092
63 100000 4.61169E+18 46116860184273900 46116860184
64 100000 9.22337E+18 92233720368547800 92233720369
30
DAY..3000000.........1073741823......10737418.....................11
TOTAL
64
DAY..6400000.........1.84467E+19.....184467440737095000......184467440737
TOTAL
YOUR GAIN IN 30 DAYS = 8 MILLION POUNDS..GOT IT BUT
ONLY BE CAREFULL THAT YOUR FRIEND WONT RUN OUT OF YOU
ON THE 25 TH. DAY.!!!
YOUR GAIN IN 30 DAYS = 184467440731 MILLION POUNDS
NOW COMING TO THE MATHS PART OF THIS ,THIS SEQUENCE
WHERE EACH NUMBER BEARS A CONSTANT RATIO TO ITS
PREDECESSOR IS CALLED GEOMETRIC PROGRESSION..HERE YOU
FIND EACH NUMBER IS OBTAINED FROM THE PREVIOUS ONE BY
MULTIPLYING WITH 2 , CALLED COMMON RATIO.
THE LAST NUMBER ON NTH. DAY AND SUM OF SUCH SERIES OF
NUMBERS UPTO THE N TH.DAY IS GIVEN BY THE FOLLOWING
FORMULAE...
N TH. NUMBER = FIRST NUMBER *(C0MM0N RATIO
)^(N-1)=A*(R)^(N-1)=(2)^(N-1) IN THIS CASE.
SUM UP TO N TH.NUMBER =A*{((R)^N -
1))/(R-1)}={(2)^N-1}IN THIS CASE
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