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Old 09-26-2012, 08:07 PM   #9331
Fbone
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Golf? How many are on each team?


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12 players
1 captain and 4 assistant captains (non-playing)
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Old 09-26-2012, 10:47 PM   #9332
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And on the American team you also have Michael Jordan.
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Old 09-27-2012, 01:38 AM   #9333
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And on the American team you also have Michael Jordan.
My father was a scratch golfer. Lived and breathed for the game. Played at least 36 holes every week, only took vacations where there were highly rated courses, watched every televised match all day long if it was raining too hard to go and play himself, and practiced his putting in the living room every night. I think his greatest disapointment in life was that his son had LESS than no interest in the game. I was given lessons by the country club pros, had my own clubs, shoes, etc... I diligently listened to the pro. I tried. I practiced (Just to be fair to my folks... They would, and did, get me lessons in anything I ever wanted to learn except bagpipes) I hated every minute of it, and though I tried to hide it from them, they knew. By the age of 13 they finally stopped asking me 'did you go out today? and never signed me up for another golf lesson. From that day on, the only times I would venture out onto a golf course would be at night time during country club dances, and only as far as the second green...


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Old 09-27-2012, 02:47 AM   #9334
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Golf is a lucrative gig if you have some talent. Last week Brandt Snedeker won $1.44 million in the Coca Cola Tour Championship. Not bad for four days work. He also received $10 million for winning the year long FedEx Cup.

A player tied for 23rd can earn $60,000 after 72 holes and those tied for 70th still grab $13,000.

And then there's all the endorsements.
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Old 09-27-2012, 03:07 AM   #9335
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But it probably cost a player $10,000 a week to play. Caddie fee, travel, accommodation, and miscellaneous. If you make the cut and end up DFL you probably just break even for that week. My father got me started and he loved having his little girl play up until I was twelve and beat him for the first time. After that it was all about the tees...
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Old 09-27-2012, 09:05 AM   #9336
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Quote:
Originally Posted by Fbone View Post
How many total gifts are given in the song, "The Twelve Days of Christmas?"
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Originally Posted by pdurrant View Post
12*1 + 11*2 + 10*3 + 9*4 + 8*5 + 7*6 + 6*7 + 5*8 + 4*9 + 3*10 + 2*11 + 1*12

= 364 gifts.
Not my place at all to pose a question, but since for the moment this seems to be in a interlude to discuss golf . . .

When I see series like this I am always interested in a general formula. So suppose instead of 12 days, your true love gives you 365 days of gifts, under the same sort of progression. First day one gift, second day two gifts and repeat of the first day gift, etc. How many total gifts at the end?

This is not the official question so do not let it interrupt the next in line.
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Old 09-27-2012, 09:40 AM   #9337
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Originally Posted by Hamlet53 View Post
Not my place at all to pose a question, but since for the moment this seems to be in a interlude to discuss golf . . .

When I see series like this I am always interested in a general formula. So suppose instead of 12 days, your true love gives you 365 days of gifts, under the same sort of progression. First day one gift, second day two gifts and repeat of the first day gift, etc. How many total gifts at the end?

This is not the official question so do not let it interrupt the next in line.
Rambling real-time working out of formula in spoiler tags for brevity.
Spoiler:
OK, the way to work it out is like this:

On the 1st day you get 1
On the 2nd day you get 2 + 1
On the 3rd day you get 3 + 2 + 1
.
.
On the nth day you get n+(n-1)+...+1

Now the sum n+(n-1)+...+1 = n(n+1)/2

So to get the total we need to add up

1*2/2, 2*3/2, 3*4/2, ... , n(n+1)/2

Obviously the factor of two is common, so we can simplify to

(1*2 + 2*3 + 3*4 + ... + n*(n+1))/2

Which looks complex, and we'll make it more complex still by remembering the general formula for each term and expanding that.

((1*1+1) + (2*2+2) + (3*3+3) + .... + (n*n + n))/2

But now we can split it into two sequences

((1*1) + (2*2) + (3*3) + .... (n*n))/2 + (1 + 2 + 3 + ... + n)/2

Now the second bit is just n(n+1)/4 (we used the same formula above).

And there is a formula for the sum of squares, so the first bit is just n(n+1)(2n+1)/12 (Proof of the sum of squares formula can be found here.)

So the total number of presents for any n days is

n(n+1)(2n+1)/12 + n(n+1)/4 which simplifies to

n(n+1)(2n+4)/12 which simplifies to:


n(n+1)(n+2)/6

A remarkably pleasing result, which could probably be derived more simply.

Check for 12: 12*13*14/6 = 364.

So for 364 days: 364*365*366/6 = 8,104,460

Last edited by pdurrant; 09-27-2012 at 01:53 PM.
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Old 09-27-2012, 09:43 AM   #9338
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8,171,255 for 365 days.

S DAYS=365,GIFTS=1,TOTAL=0
F I=DAYS:-1:1 S TOTAL=TOTAL+(I*GIFTS),GIFTS=GIFTS+1
W TOTAL




Last edited by Daithi; 09-27-2012 at 09:46 AM. Reason: added the program to find the total
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Old 09-27-2012, 09:43 AM   #9339
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Dear Algebra,
Please stop asking us to find your X. She's not coming back.


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Old 09-27-2012, 09:44 AM   #9340
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The lucky recipient would need a warehouse in which to store it all.

You count things up really well for a mouse with such small paws.
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Old 09-27-2012, 11:33 AM   #9341
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8,171,255 for 365 days.
This is true, but for 364 days it's still 8,104,460.

S DAYS=364
S TOTAL=DAYS*(DAYS+1)*(DAYS+2)/6
W TOTAL

I think my version is a little more efficient.
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Old 09-27-2012, 12:19 PM   #9342
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Originally Posted by pdurrant View Post
This is true, but for 364 days it's still 8,104,460.

S DAYS=364
S TOTAL=DAYS*(DAYS+1)*(DAYS+2)/6
W TOTAL

I think my version is a little more efficient.
I agree completely. I also happen to like your version. Simpler is always better.

The reason I posted the 365 answer was because that was what was asked for in the question, and I did my little program at about the same time you did your post. I certainly didn't mean you any disrespect pdurrant, and I like your method to the answer better.
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Old 09-27-2012, 12:55 PM   #9343
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The reason I posted the 365 answer was because that was what was asked for in the question, and I did my little program at about the same time you did your post. I certainly didn't mean you any disrespect pdurrant, and I like your method to the answer better.
And here's where we find out whether a mouse can blush.

I mis-read the original question, and mixed up the question asked (365 days) with the answer to number of presents for 12 days (364 presents).
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Old 09-27-2012, 01:31 PM   #9344
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This has sort of changed topic. Besides no one can catch Fbone, so unless you have a specific desire to guess the remaining questions I can just reveal them.
Just let me know.
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Old 09-27-2012, 01:34 PM   #9345
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Well I don't know any of the unanswered questions, but I would like to know the answers (particularly the one about the European voted off the team because he didn't play much in Europe - I'd never heard of that at all).

I thought it was a good set of questions FWIW; certainly more interesting than a bunch of mathematical formulae
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