1. ## Pennies Anyone?

The Lincoln Cent

If you stacked pennies [U.S. Lincoln Cents] in a cube formation, six feet wide, six feet tall and six feet thick, what would be the value in U.S. Dollars? There are 100 pennies to the dollar and a good approximate answer will suffice.

2. ## Re: Pennies Anyone?

I think I have this but I am doing 3 things at the same time

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">\$164,886.75</span hide>

3. ## Re: Pennies Anyone?

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">\$108,749</span hide>

4. ## Re: Pennies Anyone?

I was looking for an approximation but I think you could be a bit closer...

5. ## Re: Pennies Anyone?

I am assuming the following values:

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold"> Diameter = 19.1 millimetres or 0.75 inches, thickness of 1 millimetre or 0.0394 inches</span hide>

6. ## Re: Pennies Anyone?

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Very, very close John. But, if approximate were to mean within 5%, you'd still be a little out of range...</span hide>

7. ## Re: Pennies Anyone?

i didn't assume <img src=/S/laugh.gif border=0 alt=laugh width=15 height=15>

US penny

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">it lists the thickness at .061 in (1180 high)</span hide>

8. ## Re: Pennies Anyone?

JB: <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">The cube could not be entirely filled. Round objects would create gaps.</span hide>

I haven't actually done the experiment. I was going to but I could only accumulate 185 pennies... The solution can be found here

<img src=/S/cheers.gif border=0 alt=cheers width=30 height=16>

9. ## Re: Pennies Anyone?

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">108,748.80</span hide>
So I agree with <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">John</span hide>
using <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">.75" = diameter; .061" = thickness</span hide>

10. ## Re: Pennies Anyone?

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">72 inches divided by .061 inches = 1180.3278 which would add more, but 1180.3278, or 1181 can't fit in the cube, only 1180 can</span hide>

11. ## Re: Pennies Anyone?

OK

I will adjust my answer to 1.55mm as the assumed thickness to <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">\$106,314.50</span hide>

solution attached

12. ## Re: Pennies Anyone?

<P ID="edit" class=small>(Edited by gdrezek on 01-Nov-06 11:03. added more "precise" value for thickness)</P>I think the conversions are skewing the answers......

if you use 0.061023622 as the thickness the answer is <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">\$108,656.64</span hide>

13. ## Re: Pennies Anyone?

<img src=/S/grin.gif border=0 alt=grin width=15 height=15>

I agree, the maths is very simple but I would love to know why the website in the link above makes it \$110K but at least we all agree on the method.

14. ## Re: Pennies Anyone?

I think the folks on the website were committed to keeping the pennies organized in neat stacks, whereas the puzzle I presented did not specifically require that. I suppose we could melt down the pennies to form a more solid cube <img src=/S/smile.gif border=0 alt=smile width=15 height=15> Who knows?

It's the day after Halloween so abundant choccy for all participants.

15. ## Re: Pennies Anyone?

If you stack a little more densely, you can put more in. If you stacked the pennies neatly in stacks where they were in hex formation I get \$123959. 72"/.75" =96 in first row, 95 in second 96 in third, 95 in 4th, etc, for a total of 110 rows (set up hexagons, first row width sqrt(3)/2, each additional row 3*sqrt(3)/8). This gives 55*(96+95)*1180 pennies.

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