This week's maths problem

Problem of the week

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On Friday of each week we will post a new maths challenge.
You may submit your solution by the following Thursday.
Each problem contains two different levels of difficulty. You will be awarded from 2 to 12 points for a full answer.
Each series contains 12 problems before the stage winner is determined.
Your score will be published here.

In each series we will give away 3 books as prices. The prices will be drawn by lot among the best ten participants of the series. The books are kindly sponsored by Buchdienst Rattei of Chemnitz.

Suggestions for problems are welcome.

Deadline is 1th of March 2018.


German version - Italian version - French version - Spanish version

 

Series 47

problem 559

“Is it time alrteady for picking oranges in Sicily?”, Bernd’s granddad asked in surprise.
“Yes, time flies and it’s about time our hard working orange pickers created some nice patterns for recreation”, Maria replied.
“Let’s see.“

559


In the picture you can see stages 1, 2 and 3 of these quickly developing stars.
Stage1: one orange (here blue)
Stae 2: There is a hexagon around the orange of stage 1 (red) and six more oranges as the points of a star (green – forming a triangle with the red oranges).
Stage 3: The green oranges of stage 2 are completed into a hexagon and then more blue and red to create triangualar points again.
In stage 4 the buke oranges would be completed to form another hexagon and then we’d again create the points of the star.
How many oranges will be needed for stage 4 and stage 5? - 4 + 5 blue points
Which stage would need 1100 oranges? - 4 red points
How many oranges do you need to arrange n stages (not the n-th stage but all the oranges for n stages together). - another 5 red points 
               


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You can also send a paper copy of your solution as long as it is postmarked on or before the deadline.
adress:
Thomas Jahre
Stollberger Strasse 25
09119 Chemnitz
Germany


Links:

http://www.wurzel.org/

https://www.facebook.com/ArchimedesLab

http://people.missouristate.edu/lesreid/potw.html

post address:

Thomas Jahre
Chemnitzer Schulmodell
Stollberger Straße 25
09119 Chemnitz
Deutschland/Germany
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