This week's maths problem

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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 December 2022.

German version - Italian version - French version - Spanish version  Hungarian Version Russian version  --> 中文/Chinese <--

Series 61

problem 731

"I got lots of sticky dots, red and blue ones. Now I am trying out how many ways there are to get different patterns," said Maria.
Figure 1. The sticky dots form the corners of an equilateral triangle.
Possibility 1: only red dots, possibility 2: 2 red, 1 blue, - counts as one pattern, because turning or mirroring does not count as a new pattern.
Possibility 3: 2 blue, 1 red and possibility 4 all blue.
How many possibilities are there if the sticky dots form a regular pentagon? 3 blue points
How many possibilities are there if the sticky dots form a regular hexagon? 3 red points

-> Enigma <--

https://www.schulmodell.eu/images/stories/mathe/horst/raetsel.php

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adress:
Thomas Jahre
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09119 Chemnitz
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