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 11nd. December 2025
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Series 71
problem 843
Grandpa shows Bernd and Maria a photograph of a star glued together from wooden strips, which he built himself years ago. The outline has the shape of a pentagram and its points [AF], [FB], ... [KA] are 8 cm long. He says: ‘In this photograph, you can see that a smaller star in the shape of a pentagram is “missing” in the centre of the star, which was created from the large star by centric stretching with the centre M. The area of the “hole” is 1/16 of the area of the complete star.’
①Calculate the lengthof the points auf the „cut out“ star! (A'F'=F'B' = ... = K'A') [2 blue points]
The illustration shows that the ‘star with a star-shaped hole’ is glued together from 10 congruent quadrilaterals. (for example, AFF'A')
② Explain why each of these quadrilaterals is a trapezium, and calculate the length of the trapezium side [FF']. Finally, calculate the distance between the two parallel sides of the trapezium, i.e. the width of the wooden strip from which the “star with a star-shaped hole” was made. [6 red points]
Deadline for solution is the 11st. December 2025.
-> Enigma <--
https://www.schulmodell.eu/images/stories/mathe/horst/raetsel.php
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adress:
Thomas Jahre
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Germany
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