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        riddles >> microsoft >> Quarter Stacking Riddle
        
(Message started by: Bob Portale on Feb 5^th, 2004, 8:52am)

Title: Quarter Stacking Riddle
Post by Bob Portale on Feb 5^th, 2004, 8:52am

Title: Re: Quarter Stacking Riddle
Post by towr on Feb 5^th, 2004, 9:08am

on 02/05/04 at 08:52:16, Bob Portale wrote:

If you stacked quarters end to end, how many quarters would you need to achieve the height of the Empire State Building? Please explain how you derived this number.

I assume it's about american dollar quarters, and not one of the hundreds (or thousands) of other types of quarters. Which mean I have no idea what the average thickness is as I've never seen them..
But just height divided by thickness should give the answer.. Unless the 'end-to-end' somehow implies something other than stacking the discs into a cylinder..

Title: Re: Quarter Stacking Riddle
Post by Icarus on Feb 5^th, 2004, 7:56pm

I just measured a stack of 10 quarters with a set of calipers. The thickness was 0.663 inches, or 0.0663 inch/quarter. The official ESB website gives the height as 1,454 feet = 17,448 inches. So we have:

# of quarters * (0.0663 inches/quarter) = 17,448 inches.

Dividing by 0.0663 gives (# of quarters) = 17,448 in/(0.0663 in/quarter) [approx] 263,000.

So it would take about 263,000 quarters ([pm] 1000 or so).

Title: Re: Quarter Stacking Riddle
Post by John_Gaughan on Feb 5^th, 2004, 8:07pm

That many quarters is more than my net worth. That's not saying much ;-)

How much mass would that stack have?

Title: Re: Quarter Stacking Riddle
Post by Icarus on Feb 5^th, 2004, 9:24pm

Alas, while I happen to have a pair of calipers handy (leftover from a machinist job I had years ago), I do not have a scale of that sensitivity around. So you will have to look it up.

Title: Re: Quarter Stacking Riddle
Post by ChineseStunna on Feb 11^th, 2004, 1:28pm

Personally I think since the question has the word "Estimate" in there, that means you should try to do as they say, estimate instead of looking up stats on the internet and giving a precise answer...

my personal answer:

each quarter is a cylinder with an 1" diameter (disregard the height or thickness)
If we assume the quarters are "filled" with optimal efficiency, which means perfect stacks of 10' high with offsetting rows, the number of columns is say X.
For easier modeling purposes, we'll say the rows are lined up, so it's a perfect chess board square pattern with columns on the squares, we call this Y.

Y < X for sure, but it's easier to calculate Y.

Y is basically (4'x12)(8'x12), which is we can approximate from 48x96 to 50x100, that's 5000 stacks!

Given that the normal "floor" height of buildings are 10' high, we can then say that the number of stacks is analogue to the number of floors.

even at Y efficiency, we have about 5000 floors, even at 30% efficiency of Y, we have 1500 floors.

Even is we assuming the Empire State has double height floors, it would still take 750 floors to be talller than the closest of quarters at 30% efficiency.

So one can conclude that the stack of quaters in the closest is much much taller than the Empire State.

Title: Re: Quarter Stacking Riddle
Post by Icarus on Feb 11^th, 2004, 7:38pm

??? ??? ???
(1) The question does not say "estimate" anywhere.
(2) In order to come up with any sort of reasonable estimate, you need an idea of what sizes are involved.
(3) The question is "how many quarters would it take to make a single stack of the same height as the Empire State Building.
(4) What, exactly, are we calling "Y"? By your usage, Y must be some number, but you describe it as "a checkboard pattern". Mind giving the actual definition of the number you are talking about?
(5) After your disdain for looking up actual information, where in the world did the values 4' and 8' come from? What are they measures of, and how do they relate to the Empire State Building.
(6)
Quote:

we can then say that the number of stacks is analogue to the number of floors.

??? What in the world does THAT mean? ???
(7) I assure you that the Empire State Building does not have anywhere near 5000 floors (which - at the 10' per floor height you mentioned would require it to be nearly 10 miles tall). It doesn't even have 1500 floors. The correct number is around a tenth of that.
(8) What "closest" (do you mean closet, maybe?) of quarters are you talking about? What does it have to do with this question?

Title: Re: Quarter Stacking Riddle
Post by ChineseStunna on Feb 12^th, 2004, 1:54pm

Oh I guess I took the question from here, quoted from Wu's main site:

Suppose that I have a closet with a base area of 4ft by 8 ft, and a height of 10ft, and that the closet is completely filled with quarters. Now I take out that closetful of quarters and stack them atop each other, one by one. Will the resulting stack be higher, lower, or about the same height as the Empire State Building?

So that's where I got all my information and deductions from.

Title: Re: Quarter Stacking Riddle
Post by Icarus on Feb 12^th, 2004, 4:27pm

Ahh - that makes sense, then. Thinking it in answer to the question Bob asked, I was curious about your sobriety when posting it. But in answer to the question on the main M$ page, it is a good approach. (With the exception that your recognition of the inefficiency of the "Y" stacking method led you to make an adjustment in the wrong direction - that inefficiency means that more than 5000 10' stacks of quarters, not less.)

If Bob was intending to ask about that particular riddle, I did not pick up on it (it's been ages since I've even looked at those pages other than to search for specific problems), but simply saw the question he did ask. That one requires actual statistics to derive the answer, but as you have shown, you don't need nearly that much to answer the M$ question. A stack per square inch of floor space leads to a single stack more than 9 miles high, far taller than any building.

Title: Re: Quarter Stacking Riddle
Post by ChineseStunna on Feb 12^th, 2004, 6:33pm

I was sober when I posted yes, blame me for not reading the original post carefully, I though he simply said he had THAT question as in indentical to the one posted in the Riddles section.

Title: Re: Quarter Stacking Riddle
Post by Icarus on Feb 13^th, 2004, 9:58pm

The problem was, it has been so long since I looked at the riddles section, I had forgotten there was a Empire State Building question on it. When I saw your post I thought it was in answer to the particular question Bob asked, since this was the only question I was aware of. You must admit, as an answer to Bob's question, it doesn't make any sense. :D As an answer to the Riddle section question though, it's fine.

Title: Re: Quarter Stacking Riddle
Post by Bob on Feb 14^th, 2004, 4:47am

Someone at M$ said that one possible answer is 4... as in 4 quarters make up a whole. What do you think?

Title: Re: Quarter Stacking Riddle
Post by Icarus on Feb 14^th, 2004, 8:04am

I think that this level of thought process goes far toward, but fails to explain completely, the release of Windows ME!

http://www.bbspot.com/Images/News_Features/2003/01/os_quiz/windows_me.jpg

Title: Re: Quarter Stacking Riddle
Post by John_Gaughan on Feb 14^th, 2004, 12:27pm

Last time I took that test I was OS/2. I feel like a red-headed stepchild ;D

Title: Re: Quarter Stacking Riddle
Post by Big Rob on Mar 9^th, 2004, 6:56pm

actually the answer to this is quite simple, i didnt look up an stats at all just estimated, but even so the answer is very obvious!

lets start with the dimesions of the closet, if we break this down to inches the area of the closet floor is 48 inches by 96 inches which equals 4,608 inches. A quater is about an inch thick so one can assume that you can fit 4,608 quaters on the floor.
Now we have to estimate how many quaters stacked high will make an inch. I assume that ten quaters stacked high are about an inch. So if we multiply the number of quaters we can fit on the floor, 4,608 by ten we'll have the number of quaters you'd have to stack on the floor to make the pile an inch high, 46,080. Now there's 12 inches in a foot and the closet is ten feet high or 120 inches. So once we multiply 46,080 by 120 we can get an idea of how many quaters can fit in the closet, 5,529,600 (or $1,382,400)
Since we've already determined that ten quaters makes an inch and assuming one could stack 5,529,600 quaters, all you'd have to do to find out how tall this stack is would be divide the amount of quaters by ten, 552,960 inches or 46,080 feet!
now the empire state building is about 1,500 feet and that's to the very top of the antenna which is the highest point on the building so as you can see, this ones not even close...wether you estimate or get the exact measurement of a quater, the answer will always be the same, this stack of quaters is much much taller than the empire state building.

Title: Re: Quarter Stacking Riddle
Post by grimbal on Apr 30^th, 2004, 11:49am

Hm... it depends how you cut the Empire State Building. If you cut it horizontally, you will need all 4 quarters. If you cut it vertically just one quarter will do.

Probably not the intended answer, but if you can say that in a dead serious tone, you will certainly get points for your bullsh*t abilities.

Title: Re: Quarter Stacking Riddle
Post by Karl Varga on Oct 26^th, 2004, 1:47am

My answer is to the QUARTER STACKING ESTIMATE riddle on the MS page. It seems fairly simple to me, and I think the solutions I've seen are unnecessarily complex. Here's what I did:

(Note that you only have to say whether it's higher, lower, or about the same height as the Empire State Building, so we can estimate)

The "volume" of coins in the closet is 4x8x10 = 320 sqft. If we convert that to inches we have 320x12x12 = 46080 sqinches. Assuming that a quarter is about an inch in diameter if we stack all those inches (coin stacks) on top of eachother we have a 46080/12= 3840 ft high stack = 1280 meters, which is way bigger than the ESB, even if our estimates introduced some error. But since the estimate of a quarter being about an inch in diameter is very conservative and there's a lot of air space (round coins, square inches), the actual result would be even higher, so we're still right.

Title: Re: Quarter Stacking Riddle
Post by Icarus on Oct 26^th, 2004, 6:35pm

on 10/26/04 at 01:47:29, Karl Varga wrote:

The "volume" of coins in the closet is 4x8x10 = 320 sqft. If we convert that to inches we have 320x12x12 = 46080 sqinches.

Volume is measured in cubic inches, not square inches. The volume of the closet is 320 cu.ft or 320[times]12[times]12[times]12 = 552960 cubic inches. The coins do not fill this entire volume, however. It is impossible to fit the coins in so that no empty space remains.

Quote:

Assuming that a quarter is about an inch in diameter if we stack all those inches (coin stacks) on top of each other we have a 46080/12= 3840 ft high stack

A quarter is an inch in diameter. Does this mean you intend to stack them up standing on their sides?

I think ChineseStunna's approach is simpler:
If you allot each stack its own square inch of floor space (as when they are stacked up neatly in rows and columns), then you have (4[times]12)[times](8[times]12) = 4608 stacks, each of which is 10 feet tall, for a total of 46080 feet, or roughly 8.7 miles tall. Certainly taller than the E.S.B., or even 31 E.S.B.s.

Title: Re: Quarter Stacking Riddle
Post by Grimbal on Oct 27^th, 2004, 4:32am

To estimate the mass, just consider the volume filled with metal, and multiply by 0.7%, a rough estimate of the packing density. I wouldn't assume the coins are neatly arranged in stacks arranged in a hexagonal pattern. They are just dumped in a container.

Volume = 1.2 x 2.4 x 3 = 8.64 m³,
Density of copper and nickel is 8.9 tons/m³,
The packing density of randomly packed spheres is 64%, of randomly packed M&M's 68%. I think the flat side of coins could bring it to 70%.
So, the mass of the coins could be 53-54 metric tons.

Title: Re: Quarter Stacking Riddle
Post by coolnfundu on Nov 3^rd, 2004, 9:01pm

I have been asked this question and really would appreciate any help I can get!

If you stacked quarters end to end, how many quarters would you need to achieve the height of the Empire State Building? Please explain how you derived this number.

Perspectives:
1. They really want you to stack the coins and achieve the height, they dont want you to act cheeky and invent barometer solutions.
2. Empire State Building is the one in USA which is awfully tall and whats more awful is that you dont know its height actually and compound the problem by knowing that you dont know the height of an average coin, perhaps only its diameter. Maybe one such data can be asked, if they do provide it.
3. So what the problem can be worded to read is: How many coins would be there in a stack of a height of Empire State Building? Now I dont have a clue on how to solve that without any actual data, provided that is, this is a correct reformulation of the problem.

Title: Re: Quarter Stacking Riddle
Post by coolnfundu on Nov 3^rd, 2004, 9:09pm

on 10/26/04 at 18:35:32, Icarus wrote:

I think ChineseStunna's approach is simpler:
If you allot each stack its own square inch of floor space (as when they are stacked up neatly in rows and columns), then you have (4[times]12)[times](8[times]12) = 4608 stacks, each of which is 10 feet tall, for a total of 46080 feet, or roughly 8.7 miles tall. Certainly taller than the E.S.B., or even 31 E.S.B.s.

I am totally stuck, how did you get 4*12*8*12 approach?

Title: Re: Quarter Stacking Riddle
Post by Icarus on Nov 9^th, 2004, 9:00pm

There are two different questions being addressed in this thread.

Originally, we have Bob Portale's question in the first post. This question cannot be reasonably answered without additional information (height of E.S.B, thickness of the quarter). With this information I calculated ~263,000 in Reply #2. Alternatively, you can interpret "quarter" as being "quarter of the E.S.B." - apparently this is what Bob's M$ contact did (see reply#11).

In Reply #5, ChineseStunna mistook this thread as being about another question, which William has posted on his Riddles page:

Quote:

Suppose that I have a closet with a base area of 4ft by 8 ft, and a height of 10ft, and that the closet is completely filled with quarters. Now I take out that closetful of quarters and stack them atop each other, one by one. Will the resulting stack be higher, lower, or about the same height as the Empire State Building?

Almost all of the remainder of this thread, including the post you quoted, is addressing this question, rather than Bob's. 4*12*8*12 is area of the closet in square inches, and is a lower bound on the number of 10 ft high stacks that can be made from the quarters in the closet.

Title: Re: Quarter Stacking Riddle
Post by Holly Osborn on Dec 29^th, 2004, 8:29am

Has anyone even REALLY read Bob's post? It says "END TO END", wouldn't that mean flat-ways?
If I'm right (and I'm a woman so I know I am right - wink), then the answer would be about 21,475 quarters. You would surpass the height with that last quarter by about 1/2 of the quarter, but each quarter is 13/16 of an inch wide and at 17,448 inches in height divided by the decimal .8125 (which is what 13/16 is in decimal form) = 21,475 ;D

Title: Re: Quarter Stacking Riddle
Post by Icarus on Dec 29^th, 2004, 2:12pm

"Flat-ways" is how I interpreted it. Your interpretation is "sideways". And I would like to see you stack quarters like that. Since the question said "stack", I assumed that "end-to-end" meant in the normal face-to-face fashion. And I still do, as the round edge of a quarter has no end, while the faces can be considered as such.

Title: Re: Quarter Stacking Riddle
Post by Kyle Bennett on Jan 20^th, 2005, 1:01pm

The question on the wu riddles page asks if a 4X8 foot closet completely filled with quarters to the ceiling (10' high) would be about the same, more, or less than the hieght of the Empire State Building if the quarters were stacked in a single stack.

There's no math involved that a child could not do in his head. The height of the building is ~1500 feet. A single stack of quarters in the closet is 10' high, meaning that the empire state building is the hiehgt of 150 of these stacks. The closet has 32 sf of floor space, meaning that if it held only 5 stacks per square foot, it would be roughly the number of quarters needed to stack to the top of the ESB. Since 5 quarters placed side by side fits in a fraction of a square foot, the quarters in the closet would stack much higher than the ESB. In fact, they would probably be higher by an order of magnitude, rendering irrelevant any error in the estimate of the ESB, even the the extent of several hundered feet.

Title: Re: Quarter Stacking Riddle
Post by Lee McLemore on Mar 4^th, 2005, 12:11pm

One U.S. mint quarter is approximately 1/16 of an inch in thickness. Therefore, there are 16 quarters per inch and times 12 inches per foot will give you 192 quarters per foot. The height of the Empire State Building is easily found to be 1250 feet. Therefore, 192 quarters per foot times 1250 feet will give you 240,000 quarters. ;)

Title: Re: Quarter Stacking Riddle
Post by Icarus on Mar 4^th, 2005, 4:16pm

Measurement of a sample of 10 quarters led me to value of 1/15 of an inch:

on 02/05/04 at 19:56:56, Icarus wrote:

However, I think the difference in height between your value and mine is a matter of definition. Your number agrees with that published by the Council on Tall Buildings and Urban Habitats, who do not include antennas and such in the height, while the ESB website may have.