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| Math Challenges... solve and win e$1000 |
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| BallJacker |
 Posted: Tue Feb 06, 2007 5:05 pm Post subject: |
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Investing Manager
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I'm guessing it's 500,000,001,000,000,000 or 500 quadrillion and 1 billion, Bob, err Dave.
Example:
1 + 999,999,999 = 1,000,000,000
1,000,000,000 / 2 = 500,000,000
1,000,000,000 x 500,000,000 = 500,000,000,000,000,000
500,000,000,000,000,000 + 1,000,000,000 = 500,000,001,000,000,000 |
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| BallJacker |
| Posted: Tue Feb 06, 2007 5:39 pm Post subject: |
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Investing Manager
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| My mistake, the Guass formula is ((n+1)/2)n where "n" is 1 billion. The correct answer is 500.000.000.500.000.000.000 or 500 quadrillion 500 million. |
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| Dave Rathbun |
| Posted: Tue Feb 06, 2007 7:07 pm Post subject: |
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CFO
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It looks like you are getting a sum of the number values, not the digits.  Try reading the challenge again. You are way way high with your current guess. |
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| MrT |
| Posted: Wed Feb 07, 2007 4:03 am Post subject: |
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Investing Sr. Associate
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Glad to see this thread is back!
I believe the answer is
900,000,000*(1+2+3+4+5+6+7+8+9)+1=
40,500,000,001 |
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| Dave Rathbun |
| Posted: Wed Feb 07, 2007 4:16 am Post subject: |
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CFO
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| MrT wrote: | | Glad to see this thread is back! |
Me too.
| Quote: | I believe the answer is
900,000,000*(1+2+3+4+5+6+7+8+9)+1=
40,500,000,001 |
I believe you might be right. I will have to check the book when I get home from work today. Your answer may be correct, but your process is different. Since I don't remember the exact answer from the book I will have to look it up and post tonight as to whether you have the correct answer or not. |
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| Dave Rathbun |
| Posted: Wed Feb 07, 2007 3:33 pm Post subject: |
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CFO
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MrT, your answer is correct, and quite interestingly for me in a different form from that in the book. I've added the book solution here just for comparison.
Let us group the numbers in pairs:
0 and 999,999,999
1 and 999,999,998
2 and 999,999,997
and so on.
For each pair the digits add up to 81, and there are 500,000,000 pairs. The total of the digits therefore is:
81 * 500,000,000 = 40,500,000,000
But that leaves off the last number 1,000,000,000 whose digits add up to 1, so the grand total is 40,500,000,001
So congrats on solving the puzzle, e$1000 on its way soon. |
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| Dave Rathbun |
| Posted: Wed Feb 07, 2007 3:38 pm Post subject: e$ Challenge #49 |
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CFO
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e$ Challenge #49
Compete for e$1000! (The prize amount was increased starting with e$ Challenge #15.) Solve the puzzle and win! ... first winning answer to each puzzle. Some of the puzzles are going to be actual math problems, others require logical thinking instead. Each puzzle comes from a book I bought a while back. The rules:
- The answer in the book is final. Blame the publisher, not me, if you don't agree
- The first person to post the correct answer wins. Posting only, no PM's please.
- Edited posts are disqualified, even if you have the correct answer. The most recent (last) post by you for that puzzle is the only one that will be used, so if you need to make corrections simply enter another post for the challenge.
- You cannot win two challenges in a row, so the previous winner is not eligible for the next challenge.
- You may win more than one challenge, just not two in a row.
I will try to post one puzzle every other day. The puzzle will be posted first, then the following day (if available) a winner will be announced. Then the arguments or discussion about the solution can commence.  If no correct solution has been provided then the puzzle will be extended until a winning solution is provided. The puzzles get more challenging as we get further into the book.
Grand Prize
The book has 100 puzzles. Each individual winner gets one lottery ticket per win. Once all 100 puzzles have been posted (and solved) I will draw three winning tickets from a hat. Each winner will get to pick one of 3 mystery portfolios. The portfolio will have an initial value of e$2000 as of the end of February, 2006. Each has been invested as completely as possible into one stock from the S&P 500 chosen at random. The winners will have no idea which portfolio is worth the most. The first person drawn will get their pick of all 3 portfolios, the second drawn picks from between the two remaining, and the third drawn gets stuck (or lucky) with the last one available. The holding will be sold at current market price as of the end of the contest and the e$ transferred into your account. Your name may be drawn more than once, so the more e$ challenges you win, the better your chances of winning one of the three portfolios. 
The stocks were randomly selected and purchased at market open March 1, 2006. e$2000 worth of shares of each of them were put into a secret account. These will become the grand prize portfolios, and the final value will be determined at market close on the day the last puzzle is solved and the e$ prize awarded.
Thanks for playing
Ready?
Here's your 49th e$ Challenge Puzzle! Consider the following two math problems. On the left is an addition, on the right, a subtraction. The same two numbers are added on the left and subtracted on the right. Each letter represents a different digit. That is, if A is 3 (in all three positions) then B cannot be 3.
Find all of the digits.
| Code: |
X Y Z X Y Z
+ A B - A B
-------- -------
C D E F B G A |
Winner Hall of Fame
e$ Challenge Winner #1 Iceemaan
e$ Challenge Winner #2 nelaina
e$ Challenge Winner #3 conbrio
e$ Challenge Winner #4 geb9696
e$ Challenge Winner #5 CJ. Wentworth
e$ Challenge Winner #6 Im Not Warren Buffett
e$ Challenge Winner #7 CJ. Wentworth
e$ Challenge Winner #8 conbrio
e$ Challenge Winner #9 Im Not Warren Buffett
e$ Challenge Winner #10 conbrio
e$ Challenge Winner #11 Im Not Warren Buffett
e$ Challenge Winner #12 CJ. Wentworth
e$ Challenge Winner #13 rodder4hire
e$ Challenge Winner #14 The Jersey Devil
e$ Challenge Winner #15 conbrio
e$ Challenge Winner #16 The Jersey Devil
e$ Challenge Winner #17 emkie
e$ Challenge Winner #18 CJ. Wentworth
e$ Challenge Winner #19 InvestingMac
e$ Challenge Winner #20 emkie
e$ Challenge Winner #21 toys4tots16
e$ Challenge Winner #22 InvestingMac
e$ Challenge Winner #23 CJ. Wentworth
e$ Challenge Winner #24 nelaina
e$ Challenge Winner #25 emkie
e$ Challenge Winner #26 nelaina
e$ Challenge Winner #27 emkie
e$ Challenge Winner #28 MrT
e$ Challenge Winner #29 CJ. Wentworth
e$ Challenge Winner #30 conbrio
e$ Challenge Winner #31 MrT
e$ Challenge Winner #32 InvestingMac
e$ Challenge Winner #33 CJ. Wentworth
e$ Challenge Winner #34 Im Not Warren Buffett
e$ Challenge Winner #35 CJ. Wentworth
e$ Challenge Winner #36 MrT
e$ Challenge Winner #37 toys4tots16
e$ Challenge Winner #38 CJ. Wentworth
e$ Challenge Winner #39 MrT
e$ Challenge Winner #40 rino1
e$ Challenge Winner #41 CJ. Wentworth
e$ Challenge Winner #42 MrT
e$ Challenge Winner #43 SpiffWilkie
e$ Challenge Winner #44 MrT
e$ Challenge Winner #45 Nobody!
e$ Challenge Winner #46 prederer
e$ Challenge Winner #47 conbrio
e$ Challenge Winner #48 MrT
e$ Challenge Winner #49 ??? Your Name Here! ???
e$ Challenge Holdings Performance as of this post were: +6.43%, +8.19%, +77.54.%. The "dart board" portfolio is back in the black (considering all three holdings) with a return of 30.72% since being opened on March 1, 2006. One stock is clearly outperforming the other two by a wide margin.
Remember to spread the winnings around, the previous winner (MrT) is not elegible to win the current challenge. The next puzzle will be posted on or after Saturday, time permitting, or after this puzzle is solved, whichever comes later. Total e$ prizes paid to date: e$44,500 + One Barren Desert worth e$1125 |
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| Kiman4 |
| Posted: Wed Feb 07, 2007 6:36 pm Post subject: |
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Investing Sr. Associate
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| i've narrowed down the only possibilities but apparently none of the remaining combinations work. i'm stumped |
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| Kiman4 |
| Posted: Wed Feb 07, 2007 7:13 pm Post subject: |
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Investing Sr. Associate
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X=9
Y=6
Z=5
1=7
B=8
C=1
D=0
E=4
F=3
G=2
 e$ here i come |
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| Dave Rathbun |
| Posted: Wed Feb 07, 2007 9:44 pm Post subject: |
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CFO
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| Kiman4 wrote: | | e$ here i come |
Are you sure?  |
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| gnd0221186 |
| Posted: Wed Feb 07, 2007 11:08 pm Post subject: |
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Investing Associate
Joined: 23 Jan 2007
Posts: 47
This Month: 0
198.44 e$
Net worth: 103,886.44
Portfolio Value: 103,688.00
Monthly Return: 12.84%
Trades this month: 0
Churn Rate: 0.00%Items
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X = 9
Y = 4
Z = 5
A = 7
B = 8
C = 1
D = 0
E = 2
F = 3
G = 6
XYZ = 945
AB = 78
CDEF = 1023
BGA = 867 |
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| MrT |
| Posted: Thu Feb 08, 2007 4:26 am Post subject: |
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Investing Sr. Associate
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| Dave Rathbun wrote: | MrT, your answer is correct, and quite interestingly for me in a different form from that in the book. I've added the book solution here just for comparison.
Let us group the numbers in pairs:
0 and 999,999,999
1 and 999,999,998
2 and 999,999,997
and so on.
For each pair the digits add up to 81, and there are 500,000,000 pairs. The total of the digits therefore is:
81 * 500,000,000 = 40,500,000,000
But that leaves off the last number 1,000,000,000 whose digits add up to 1, so the grand total is 40,500,000,001
So congrats on solving the puzzle, e$1000 on its way soon. |
In case anyone is interested, I'll present my approach. Basically, I decided to count the number of 1's because that would also equal the number of 2's, 3's, etc. If we are only counting from 0to 10 (ignoring 10), there is 1 of the 1's. If we count from 0 to 100, there is 20 of the ones, from 0 to 1000 there is 30 of the ones.
So the pattern becomes x*10^(x-1) where x is the power that you are counting to, in this case, 1 billion (10^9), x=9, so it is 900,000,000 of the 1's, so there is the same number of 2,3,4,5,6,7,8 and 9's, then add the extra 1 for the number 1 billion. |
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| Dave Rathbun |
| Posted: Thu Feb 08, 2007 8:24 am Post subject: |
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CFO
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I was interested, thanks
@gnd0221186, your math looks good. I'll confirm tonight. |
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| Dave Rathbun |
| Posted: Thu Feb 08, 2007 12:08 pm Post subject: |
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CFO
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gnd0221186 has the correct answer. The answer posted earlier was very close, but the rule said that each digit was unique, meaning you cannot assign the same digit to two different letters.
e$1000 prize money on its way shortly. I will go ahead and post the next puzzle later tonight. |
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| Dave Rathbun |
| Posted: Thu Feb 08, 2007 12:26 pm Post subject: e$ Challenge #50! |
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CFO
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e$ Challenge #50
Compete for e$1000! (The prize amount was increased starting with e$ Challenge #15.) Solve the puzzle and win! ... first winning answer to each puzzle. Some of the puzzles are going to be actual math problems, others require logical thinking instead. Each puzzle comes from a book I bought a while back. The rules:
- The answer in the book is final. Blame the publisher, not me, if you don't agree
- The first person to post the correct answer wins. Posting only, no PM's please.
- Edited posts are disqualified, even if you have the correct answer. The most recent (last) post by you for that puzzle is the only one that will be used, so if you need to make corrections simply enter another post for the challenge.
- You cannot win two challenges in a row, so the previous winner is not eligible for the next challenge.
- You may win more than one challenge, just not two in a row.
I will try to post one puzzle every other day. The puzzle will be posted first, then the following day (if available) a winner will be announced. Then the arguments or discussion about the solution can commence. If no correct solution has been provided then the puzzle will be extended until a winning solution is provided. The puzzles get more challenging as we get further into the book.
Grand Prize
The book has 100 puzzles. Each individual winner gets one lottery ticket per win. Once all 100 puzzles have been posted (and solved) I will draw three winning tickets from a hat. Each winner will get to pick one of 3 mystery portfolios. The portfolio will have an initial value of e$2000 as of the end of February, 2006. Each has been invested as completely as possible into one stock from the S&P 500 chosen at random. The winners will have no idea which portfolio is worth the most. The first person drawn will get their pick of all 3 portfolios, the second drawn picks from between the two remaining, and the third drawn gets stuck (or lucky) with the last one available. The holding will be sold at current market price as of the end of the contest and the e$ transferred into your account. Your name may be drawn more than once, so the more e$ challenges you win, the better your chances of winning one of the three portfolios.
The stocks were randomly selected and purchased at market open March 1, 2006. e$2000 worth of shares of each of them were put into a secret account. These will become the grand prize portfolios, and the final value will be determined at market close on the day the last puzzle is solved and the e$ prize awarded.
Thanks for playing
Ready?
Here's your 50th e$ Challenge Puzzle! Three friends, Benjamin, Im Not Warren Buffett, and frusnak leave at the same time and place to go to a town 8 miles away.
Benjamin starts out walking. Im Not Warren Buffett takes frusnak in his car. After a certain time, frusnak gets out of the car and goes on walking. Im Not Warren Buffett drives back to Benjamin, takes him in the car, and drives him to town. All three arrive at the exact same time.
Benjamin and frusnak both walk at a constant rate of speed of 6 miles per hour. Im Not Warren Buffett drives at a constant speed of 30 miles per hour.
How long did the trip last?
Special Notes: This is the 50th of 100 total puzzles. As a result, the prize for this puzzle will not be e$1000... it will be e$1000 plus one Barren Desert property, currently worth just under e$1500. If you hold the property it increases in value, slowly but surely. The property values increase each evening. And, as a special double-bonus, if the winner of this challenge is a first-time winner in this contest, and their current net worth is under e$50,000, then I will award the e$1000 cash + the bonus Barren Desert property plus a second bonus Barren Desert property. The extended bonus is only available to first-time winners, and only if your total net worth is under e$50,000 at the time you win.
So there you go, a bit of an extra incentive. I have already purchased the extra properties and have them ready to award to the winners. Enjoy, and thanks for playing.
Winner Hall of Fame
e$ Challenge Winner #1 Iceemaan
e$ Challenge Winner #2 nelaina
e$ Challenge Winner #3 conbrio
e$ Challenge Winner #4 geb9696
e$ Challenge Winner #5 CJ. Wentworth
e$ Challenge Winner #6 Im Not Warren Buffett
e$ Challenge Winner #7 CJ. Wentworth
e$ Challenge Winner #8 conbrio
e$ Challenge Winner #9 Im Not Warren Buffett
e$ Challenge Winner #10 conbrio
e$ Challenge Winner #11 Im Not Warren Buffett
e$ Challenge Winner #12 CJ. Wentworth
e$ Challenge Winner #13 rodder4hire
e$ Challenge Winner #14 The Jersey Devil
e$ Challenge Winner #15 conbrio
e$ Challenge Winner #16 The Jersey Devil
e$ Challenge Winner #17 emkie
e$ Challenge Winner #18 CJ. Wentworth
e$ Challenge Winner #19 InvestingMac
e$ Challenge Winner #20 emkie
e$ Challenge Winner #21 toys4tots16
e$ Challenge Winner #22 InvestingMac
e$ Challenge Winner #23 CJ. Wentworth
e$ Challenge Winner #24 nelaina
e$ Challenge Winner #25 emkie
e$ Challenge Winner #26 nelaina
e$ Challenge Winner #27 emkie
e$ Challenge Winner #28 MrT
e$ Challenge Winner #29 CJ. Wentworth
e$ Challenge Winner #30 conbrio
e$ Challenge Winner #31 MrT
e$ Challenge Winner #32 InvestingMac
e$ Challenge Winner #33 CJ. Wentworth
e$ Challenge Winner #34 Im Not Warren Buffett
e$ Challenge Winner #35 CJ. Wentworth
e$ Challenge Winner #36 MrT
e$ Challenge Winner #37 toys4tots16
e$ Challenge Winner #38 CJ. Wentworth
e$ Challenge Winner #39 MrT
e$ Challenge Winner #40 rino1
e$ Challenge Winner #41 CJ. Wentworth
e$ Challenge Winner #42 MrT
e$ Challenge Winner #43 SpiffWilkie
e$ Challenge Winner #44 MrT
e$ Challenge Winner #45 Nobody!
e$ Challenge Winner #46 prederer
e$ Challenge Winner #47 conbrio
e$ Challenge Winner #48 MrT
e$ Challenge Winner #49 gnd0221186
e$ Challenge Winner #50 ??? Your Name Here! ???
e$ Challenge Holdings Performance as of this post were: +4.44%, +9.42%, +75.61.%. The "dart board" portfolio is back in the black (considering all three holdings) with a return of 29.82% since being opened on March 1, 2006. One stock is clearly outperforming the other two by a wide margin.
Remember to spread the winnings around, the previous winner (gnd0221186) is not elegible to win the current challenge. The next puzzle will be posted on or after Saturday, time permitting, or after this puzzle is solved, whichever comes later. Total e$ prizes paid to date: e$45,500 + One Barren Desert worth e$1125 |
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