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Cool Contest But No Answer

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southsav
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 Posted 02/03/2012  9:55 pm Show Profile Bookmark this topic Add southsav to your friends list Get a Link to this Message


Saw this cool photo tonight and wondered how many quarters and how long it took to do this. There are about 16 columns with highest having about 100 coins in it (unless I lost count when I sneezed)

You can guess, but I don't have the answer unless you want to try it at home.


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 Posted 02/03/2012  10:53 pm  Show Profile Check Earle42's eBay Listings Bookmark this reply Add Earle42 to your friends list Get a Link to this Reply
If each of these piles was contorted into straightened columns, according to your count, you would have 100 in the tallest.

It appears that each stack is just one quarter taller than the others.

So, in effect, you have 16 stacks - the smallest having (100-15=) 85 and the tallest having 100.

Making it easier, you have 16 stacks of 85 (= 1,360) and the 1st column has 0 extra; the 2nd has 1 extra, the 3rd has 2 extra, the 4th has 3 extra, ..., the 15th has 14 extra, the 16th has 15 extra etc.

Let's employ an old trick for totaling the extras easily. Line the extras (only) from the columns up smallest to tallest; add the outermost + innermost stacks; and work our way toward the center - makes it easy to see total of extras will simply be 8 sets of 15:

Stack#......Extra coins.........Stack#...........Extra coins.............extra + extra = 15
1...............0.......................16.................15...........................0+15=15
2...............1.......................15.................14...........................1+14=15
3...............2.......................14.................13...........................2+13=15
4...............3.......................13.................12...........................3+12=15
5...............4.......................12.................11...........................4+11=15
6...............5.......................11.................10...........................5+10=15
7...............6.......................10..................9............................6 + 9=15
8...............7.........................9..................8............................7 + 8=15


So 8x15 extras + 1360 in each stack =
120 + 1360 = 1480

So if my meds did not hinder my clarity of thought - although it takes a lot of writing to explain, its not so hard to figure out when you untwist the stacks.
Visualize Whirled Peas
- Doctors with patience will lose money letting loose their patients.
- They're over there with their car.
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 Posted 02/04/2012  12:03 am  Show Profile Bookmark this reply Add Cajunlady0 to your friends list Get a Link to this Reply
I keep counting 17 stacks each time I look at it........not 16. Unless, it is an optical illusion.
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 Posted 02/04/2012  12:09 am  Show Profile Bookmark this reply Add Fuzzy317 to your friends list Get a Link to this Reply
I count 17 columns
17th column = 100 coins
16th column = 99 coins
.
.
1st column = 84 coins
======================
should be 1564 coins = $391.00
Edited by Fuzzy317
02/04/2012 12:14 am
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 Posted 02/04/2012  07:53 am  Show Profile Bookmark this reply Add southsav to your friends list Get a Link to this Reply
Ah hah, I knew there were some math majors here!

I told you I sneezed and may have lost count. I think you got it figured out Earle.

Cajun and Fuzzy, you are probably right.

to you all
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 Posted 02/04/2012  08:00 am  Show Profile Bookmark this reply Add f16 to your friends list Get a Link to this Reply
Yeah there are 17 columns
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 Posted 02/04/2012  4:50 pm  Show Profile Check Earle42's eBay Listings Bookmark this reply Add Earle42 to your friends list Get a Link to this Reply
17?

That would mean 17 stacks and the smallest being (100-16) = 84

The 17 columns of 84 coins = 1428 total in the equal sized stacks

The number of extras is 0 on top of the first,1 on the second ,2 on the third and so on...,3, ...,14,15,16

so this time we have:
column 1 extras + column 17 extras = 0+16=16
column 2 extras + column 16 extras = 1+15=16
column 3 extras + column 15 extras = 2+14=16
column 4 extras + column 14 extras = 3+13=16
column 5 extras + column 13 extras = 4+12=16
column 6 extras + column 12 extras = 5+11=16
column 7 extras + column 11 extras = 6+10=16
column 8 extras + column 10 extras = 7 + 9=16
column 9 extras = 8

Extras = (8x16)+9 = 128 +9=136 total extras

1428+136=1564

I enjoy problem solving of any kind.

Make it even simpler:
Call the number of stacks N

If N is odd, the total number of extras is N
and the total of coins in the same sized stacks is 101xN - (NxN)

Combined "extras + same" for odd number of stacks:
102xN - (NxN)

If N is even, the total number of extras is 1/2xN
and the total of coins in the same-sized stacks is 101xN - (NxN)

Combined "extras + same" for even number of stacks:
101.5xN - (NxN)


Yes, I enjoy problem solving - this was fun

Edited in green to show my error. I had a 9 instead of 8 extra in column 9
Visualize Whirled Peas
- Doctors with patience will lose money letting loose their patients.
- They're over there with their car.
Edited by Earle42
02/04/2012 5:59 pm
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 Posted 02/04/2012  4:59 pm  Show Profile Bookmark this reply Add Cajunlady0 to your friends list Get a Link to this Reply
Fuzzy and Earle are going to have to battle it out. They are off by one.

I am not even gonna try to figure out what yall said. That might cause me to have a pain.

I am just proud of myself for counting to 17. :)
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 Posted 02/04/2012  5:51 pm  Show Profile Bookmark this reply Add southsav to your friends list Get a Link to this Reply
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 Posted 02/04/2012  5:58 pm  Show Profile Check Earle42's eBay Listings Bookmark this reply Add Earle42 to your friends list Get a Link to this Reply
Fuzzy was right - I typed an 8 instead of a 9 when I made my chart of extras. So I used the 8 for the math. His total and mine now are the same.

Figures - the real easy part I missed!

Visualize Whirled Peas
- Doctors with patience will lose money letting loose their patients.
- They're over there with their car.
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 Posted 02/06/2012  1:32 pm  Show Profile Bookmark this reply Add bradez72 to your friends list Get a Link to this Reply
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 Posted 02/07/2012  10:01 pm  Show Profile Bookmark this reply Add FlipOfACoin to your friends list Get a Link to this Reply
That is an ASTOUNDING work of art! I have an 'education' in Finance and I am not even able to come up with an equation to find the answer!
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 Posted 02/17/2012  12:37 pm  Show Profile Bookmark this reply Add augold to your friends list Get a Link to this Reply


probably glued together, but still a feat of patience!
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 Posted 02/23/2012  10:42 pm  Show Profile Bookmark this reply Add biggfredd to your friends list Get a Link to this Reply
, augold!

When we sold beer cans, I'd make window displays like an inverted pyramid and my favorite, a rainbow. Very simple, but would stop people in their trax.
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 Posted 02/23/2012  11:00 pm  Show Profile Check oih82w8's eBay Listings Bookmark this reply Add oih82w8 to your friends list Get a Link to this Reply
never mind, my brain is about fried tonight...still a cool piece of art!
oih82w8 = "Oh I Hate To Wait"

"I tell her coins keep me off the streets and out of the bars." Moe145

"WOO-SAA...WOo-SAa...Woo-Saa" (calm down)
Edited by oih82w8
02/23/2012 11:03 pm
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 Posted 03/28/2012  5:26 pm  Show Profile Bookmark this reply Add bjones to your friends list Get a Link to this Reply
That's interesting and all, but more importantly, how many are pre-'64?
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