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Cut a pentagonal cake into 7 equal pieces


Best Answer TimeSpaceLightForce, 04 March 2014 - 02:14 PM

Spoiler for min slices
Go to the full post


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9 replies to this topic

#1 bonanova

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Posted 03 March 2014 - 02:20 AM

It's  your birthday, and a cake has been brought to your table, frosted on the top and sides.

The cake is 3" high and has a base in the shape of a regular pentagon, 3" on a side.

 

It's your task to cut the cake into pieces for yourself and your six guests.

You want each piece to have the same volume and the same amount of frosting.

 

The cutting is conventional: as seen from above, the cuts are like spokes radiating from the pentagon's center.

The cutting planes are perpendicular to the cake's base.

 

You realize that if you had invited two fewer guests (5 people in all) your job would be much easier.

But after some thought you devise a plan that gets the job done.

 

How do you cut your cake to provide seven pieces with equal volume and frosting?


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#2 BMAD

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Posted 03 March 2014 - 02:54 AM

tongue in cheek  :thanks:

 

cook an additional cake that completely encapsulates the pentagon with the exact same type of icing as the other cake.  place the cake around the cake to make a square.  cut the cake into 7 equal strips.

 

Op solved

 

tongue removed from cheeck


Edited by BMAD, 03 March 2014 - 02:55 AM.

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#3 BMAD

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Posted 03 March 2014 - 11:50 AM

Spoiler for for starters


Edited by bonanova, 04 March 2014 - 12:06 PM.

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#4 Rainman

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Posted 03 March 2014 - 12:24 PM

Haha, it is actually my birthday today when you posted this :P
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#5 bonanova

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Posted 03 March 2014 - 02:00 PM

HBTY, HBTY, HBDR, HBTY!

 

Cake may arrive later in the day.


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#6 bonanova

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Posted 04 March 2014 - 12:06 PM

Spoiler for for starters

 

You must be a mathematician. "This reduces to the previous case." ;)


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#7 bonanova

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Posted 04 March 2014 - 12:08 PM

Spoiler for Hint -


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#8 TimeSpaceLightForce

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Posted 04 March 2014 - 02:14 PM   Best Answer

Spoiler for min slices

Edited by TimeSpaceLightForce, 04 March 2014 - 02:15 PM.

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#9 harey

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Posted 04 March 2014 - 03:58 PM

Spoiler for ?


Bonus question for those who are at ease with formulae: Using this proceeding, in how many parts can you cut the cake at most?


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#10 TimeSpaceLightForce

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Posted 04 March 2014 - 07:55 PM

Spoiler for

 


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