## 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 2nd**

**of May 2019.**

German version - Italian version - French version - Spanish version

**Series 51**

### problem 603

“In an last year’s issue of the “Wurzel” mathematical magazine → http://wurzel.org/ ← I read something about a special kind of sorting problem. I have reconstructed this with some coloured cuboids.”

“As I see the cuboids are all of different size. I guess they have to be stacked from big to small.”

“That’s right. To do this I have a very thin piece of wood, that I can insert between any two cuboids an so turn around whatever is on top of this slat. When you look at the three depicted possibilities this means that that I don’t have to do a thing about the first stack. The two other stacks can each be turned in one go. I just have to insert the slat under the red cuboid.”

“So it’s allowed to turn a complete stack?” Bernd asked.

“Yes”, his sister answereed.

Here you can see five cuboids of different sizes (A>B>C>D>E). How many different ways are there to stack them? How many of these stacks can be turned into a correct stack in one go? - (2+2 blue points)

How many moves z do you need at most to sort a stack of n cuboids of different size? (Some assume z<=2n-3 for n>1, but is there proof?) - 4 red points.

Another red point is awarded for a stack of five cuboids (n=5) that can be sorted in exactly 5 moves.

**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. ©HRGauern[at]@t-online.de**

Send your solutions to **Diese E-Mail-Adresse ist vor Spambots geschützt! Zur Anzeige muss JavaScript eingeschaltet sein!, **if your answer contains attachments.

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adress:

Thomas Jahre

Stollberger Strasse 25

09119 Chemnitz

Germany

Links:

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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## Kommentare

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most up-to-date reports.

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goals.

nice woek fellows.

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