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 23th of August 2018.

German version - Italian version - French version - Spanish version

Series 48

problem 574

“Let’s construct something”, Lisa said to Mike.
“Any suggestions?”
Lisa draws a square ABCD (a=5cm). The she constructs a point P inside the square which is 4 cm from point A and 3 cm from point B. How far is P from C and D? (solution by construction and measuring - 3 blue points, 5 blue points for calculating)
Mike is thinking about something different. He defines a point P and is trying to find rectangles so that BP=18 cm, PC=10 cm and PD=26 cm. Somewhere he has read that in that way distance AP is always the same. How can you show that for any position of P? - 7 red points. How big – area – is such a rectangle if P is part of one of the rectangle’s sides? - another 5 red points

Solving the picture-puzzle will get you two extra blue points, provided you also got points doing the regular maths problem.
The rule for each picture puzzle is: Each icon represents one digit, same icons, same digits, different
icons, different digits. Only this numbers are present: 14, 56. ©HRGauern[at]@t-online.de

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adress:
Thomas Jahre
Stollberger Strasse 25
09119 Chemnitz
Germany

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