• #### Place five pennies on a table top, all in mutual contact.

From henhanna@gmail.com@21:1/5 to All on Thu Jun 30 06:59:59 2022
Place five pennies on a table top, all in mutual contact. (obviously, they must stack) ----------- a true, classic gem of a puzzle. i wish i knew this puzzle when i was young !

--------------- for those who know the answer already... the puzzle would be to figure out what was meant by (obviously, they must stack)
------------------------- i think i finally get it.....

"Give fire to a man, and he's warm for an hour.
Set fire to a man, and he's warm for the rest of his life."

---------- give me (us) another clever quote like this one.

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* Origin: fsxNet Usenet Gateway (21:1/5)
• From leflynn@21:1/5 to henh...@gmail.com on Sun Jul 3 16:55:07 2022
On Thursday, June 30, 2022 at 10:00:02 AM UTC-4, henh...@gmail.com wrote:
Place five pennies on a table top, all in mutual contact. (obviously, they must stack) ----------- a true, classic gem of a puzzle. i wish i knew this puzzle when i was young !

--------------- for those who know the answer already... the puzzle would be to figure out what was meant by (obviously, they must stack)
------------------------- i think i finally get it.....

"Give fire to a man, and he's warm for an hour.
Set fire to a man, and he's warm for the rest of his life."

---------- give me (us) another clever quote like this one.

Well, the only solutions I can find for five US pennies has just one of them touching the table
and they are not physically stable.

I have only been able to balance them in the approximate position as needed by using
multiple assisting pennies and a piece of tape to form a hinge between two of them.

I modeled each penny as a circular cylinder with diameter 19.05 mm and thickness 1.52 mm
If the thickness of a penny were 1.53 mm and the diameter remained the same,
I would not find a solution of this form.

Below is an IDL code to create a helpful figure.
L. Flynn

; Set constants for the penny
dp=19.05 & rp=dp/2.0 & tp=1.52

; Build a unit circle centered at the origin.
t=!pi*dindgen(2001)/1000.
x=cos(t) & y=sin(t)

; Build the base penny's top at z=0.0
x0=x & y0=y & z0=y*0.0

; Build two pennies on top of the base penny and touching in the
; middle. Make these 3-D as the positions of their tops and bottoms matter. x1=x0+1 & y1=y0 & z1=z0
x1=[x1,x1] & y1=[y1,y1] & z1=[z1,z1+tp/rp]
x1p=[x1(1000:4000),x1(0:1000)] & y1p=[y1(1000:4000),y1(0:1000)] & z1p=[z1(1000:4000),z1(0:1000)]
x2p=-x1p & y2p=y1p & z2p=z1p

; Build a pair of pennies forming a "tent" and resting on the base penny.
; Note: these are not quite in the proper position.
; Their lower edges need to be moved minutely toward the origin
; So that they touch the edges of the second and third pennies.
x3=x0 & y3=0.5*y0+0.5 & z3=sqrt(3.0)*(1.0-y3) x3p=[x3(1500:2000),x3(0:1500),x3(1500:2000),x3(0:1500)] & y3p=[y3(1500:2000),y3(0:1500),-y3(1500:2000),-y3(0:1500)] & z3p=[z3(1500:2000),z3(0:1500),z3(1500:2000),z3(0:1500)]

; Make a 3-D figure c=plot3d([x0,x1p,x2p,x3p],[y0,y1p,y2p,y3p],[z0,z1p,z2p,z3p],xrange=[-2,2],yrange=[-2,2],zrange=[0,4],axis_style=4)

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From henhanna@gmail.com@21:1/5 to leflynn on Sun Jul 3 21:26:48 2022
On Sunday, July 3, 2022 at 4:55:09 PM UTC-7, leflynn wrote:
On Thursday, June 30, 2022 at 10:00:02 AM UTC-4, henh...@gmail.com wrote:
Place five pennies on a table top, all in mutual contact. (obviously, they must stack) ----------- a true, classic gem of a puzzle. i wish i knew this puzzle when i was young !

--------------- for those who know the answer already... the puzzle would be to figure out what was meant by (obviously, they must stack)
------------------------- i think i finally get it.....

"Give fire to a man, and he's warm for an hour.
Set fire to a man, and he's warm for the rest of his life."

---------- give me (us) another clever quote like this one.

Well, the only solutions I can find for five US pennies has just one of them touching the table
and they are not physically stable.

I have only been able to balance them in the approximate position as needed by using
multiple assisting pennies and a piece of tape to form a hinge between two of them.

I modeled each penny as a circular cylinder with diameter 19.05 mm and thickness 1.52 mm
If the thickness of a penny were 1.53 mm and the diameter remained the same, I would not find a solution of this form.

Below is an IDL code to create a helpful figure.
L. Flynn

; Set constants for the penny
dp=19.05 & rp=dp/2.0 & tp=1.52

this part (above) is interesting.
you're right... if a penny was much thicker, we'd not have a solution.

i'm 90% sure that you have the canonical answer.

; Build a unit circle centered at the origin.
t=!pi*dindgen(2001)/1000.
x=cos(t) & y=sin(t)

; Build the base penny's top at z=0.0
x0=x & y0=y & z0=y*0.0

; Build two pennies on top of the base penny and touching in the
; middle. Make these 3-D as the positions of their tops and bottoms matter. x1=x0+1 & y1=y0 & z1=z0
x1=[x1,x1] & y1=[y1,y1] & z1=[z1,z1+tp/rp]
x1p=[x1(1000:4000),x1(0:1000)] & y1p=[y1(1000:4000),y1(0:1000)] & z1p=[z1(1000:4000),z1(0:1000)]
x2p=-x1p & y2p=y1p & z2p=z1p

; Build a pair of pennies forming a "tent" and resting on the base penny.
; Note: these are not quite in the proper position.
; Their lower edges need to be moved minutely toward the origin
; So that they touch the edges of the second and third pennies.
x3=x0 & y3=0.5*y0+0.5 & z3=sqrt(3.0)*(1.0-y3) x3p=[x3(1500:2000),x3(0:1500),x3(1500:2000),x3(0:1500)] & y3p=[y3(1500:2000),y3(0:1500),-y3(1500:2000),-y3(0:1500)] & z3p=[z3(1500:2000),z3(0:1500),z3(1500:2000),z3(0:1500)]

; Make a 3-D figure c=plot3d([x0,x1p,x2p,x3p],[y0,y1p,y2p,y3p],[z0,z1p,z2p,z3p],xrange=[-2,2],yrange=[-2,2],zrange=[0,4],axis_style=4)

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)
• From leflynn@21:1/5 to henh...@gmail.com on Mon Jul 4 03:16:17 2022
On Monday, July 4, 2022 at 12:26:49 AM UTC-4, henh...@gmail.com wrote:
On Sunday, July 3, 2022 at 4:55:09 PM UTC-7, leflynn wrote:
On Thursday, June 30, 2022 at 10:00:02 AM UTC-4, henh...@gmail.com wrote:
Place five pennies on a table top, all in mutual contact. (obviously, they must stack) ----------- a true, classic gem of a puzzle. i wish i knew this puzzle when i was young !

--------------- for those who know the answer already... the puzzle would be to figure out what was meant by (obviously, they must stack)
------------------------- i think i finally get it.....

"Give fire to a man, and he's warm for an hour.
Set fire to a man, and he's warm for the rest of his life."

---------- give me (us) another clever quote like this one.

Well, the only solutions I can find for five US pennies has just one of them touching the table
and they are not physically stable.

I have only been able to balance them in the approximate position as needed by using
multiple assisting pennies and a piece of tape to form a hinge between two of them.

I modeled each penny as a circular cylinder with diameter 19.05 mm and thickness 1.52 mm
If the thickness of a penny were 1.53 mm and the diameter remained the same,
I would not find a solution of this form.

Below is an IDL code to create a helpful figure.
L. Flynn

; Set constants for the penny
dp=19.05 & rp=dp/2.0 & tp=1.52
this part (above) is interesting.
you're right... if a penny was much thicker, we'd not have a solution.

i'm 90% sure that you have the canonical answer.
This shows the solution for five equally sized coins.