Nicholas' house

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The House of Santa Claus is a character game and puzzles for children. The aim is to draw a "house" in a line consisting of exactly eight lines without going through a line twice. The drawing is accompanied by the simultaneously spoken rhyme of eight syllables : "This is the house of Ni-ko-laus."

origin

A history or ancestry of this drawing game is not known. There is also the saying “If you can't do this, you won't get a husband”, which could indicate a reputation as early as the end of the 19th century.

variants

There are also variants:

  • the drawing of two houses, accompanied by the saying "This is the house of Ni-ko-laus and next to that of Santa Claus."
  • the drawing of a house with a garage and a flag, the saying is "This is the house of the Ni-ko-laus with a garment and a cap on it."
  • the drawing of two houses, a street and another house, accompanied by the saying “This is the house of the Ni-ko-laus and next to that of the Santa Claus and across the street that of the Easter hat '. "
  • the drawing of three houses, the first according to the “NAZ method” (drawing these letters), then a building (without an inside “X”) with a roof and another building (without an inside “X”) without a roof with the slogan : "This is the Ni-ko-laus house, with annex and toilet-let-ten-house."
  • the drawing of two houses, the second adjacent, built the same, but smaller, with the saying: "This is St. Nicholas' house, and his toilet is also very nice."
  • drawing two houses and a tree; the saying goes: "This is the house of Santa Claus and next door of Santa Claus with a little tree on it."

Mathematics reference

A black drawn square with its two diagonals is shown on a white background. A black right-angled triangle drawn upwards is connected to the upper side of the square, the hypotenuse of which coincides with the upper side of the square. The triangle forms, so to speak, the “roof” of the “house”. The four corner points of the square and the point with the 90 ° angle of the triangle are marked by small red dots. These red points are labeled with black numbers: The lower left corner of the square is with "1", the remaining three points of the square are counterclockwise with "2", "3" and "4" and the 90 ° degree The “roof” point of the triangle is marked with “5”.
All of them, a total of 44 solutions, are shown for the house of St. Nicholas, if the starting point is on the bottom left.
All 44 solutions with starting point 1
(▶ watch as video)
A total of 10 invalid attempts are shown for the house of St. Nicholas, with the starting point on the bottom left.
All 10 invalid attempts with starting point 1
(▶ view as video)

From a mathematical point of view, Nikolaus's house is a problem from graph theory . The object of the problem is a graph for which an Euler path but no Euler circle exists, since it contains two nodes of odd degree (nodes 1 and 2 each have a degree of 3). Complete with just one line, the house can only be drawn from node 1 or from node 2 and then ends in the other node. These two nodes have an odd number of edges (= connecting lines), while all other nodes have an even number. A solution can therefore only be found if these nodes serve as the start or end point.

The intersection point S of the two diagonals (or the inner “X”) is not a knot here, as the rules of the game do not allow you to change the direction of the line when drawing at this point. The "X" must therefore neither come from the lines [1, S , 4] (or [4, S , 1]) and [2, S , 3] (or [3, S , 2]) nor from [1, S , 2] (or [2, S , 1]) and [3, S , 4] (or [4, S , 3]), but must be composed of [1, S , 3] (or [3, S , 1]) and [2, S , 4] (or [4, S , 2]).

Finding all possible solutions is a popular exercise in algorithm technology for practicing the backtracking method. Assuming that you start at node 1, there are 44 solutions (see the illustration of all 44 solutions), and there are only 10 possibilities to play the game to lose". The possibilities that you have with node 2 as a starting point correspond to these possibilities as mirror images , whereby the mirror axis runs through the two points 5 and S , so that there are a total of 88 different ways to finish the house in one go.

Art and entertainment receptions

In 1986 the artist Reinhold Braun took up the Nikolaus house as a theme. The painting is in the administrative court of Baden-Württemberg . In 2013 it was artistically taken up in Nils Franke's oil painting Junge . This work received the Heise Art Prize 2013 and was exhibited in the Bayer Kulturhaus.

literature

  • Manfred Nitzsche: Graphs for Beginners. Around the house of Nicholas. In: Studies . 3rd, revised and expanded edition. Vieweg + Teubner, Wiesbaden 2009, ISBN 978-3-8348-0813-4 .

Web links

Commons : Haus vom Nikolaus  - Collection of images, videos and audio files

Individual evidence

  1. ↑ Michael Behrisch, Amin Coja-Oghlan, Peter Liske: The Eulertour: How Leonhard Euler draws the house of Nicholas. In: Chair of Computer Science 1. RWTH Aachen University , accessed on March 18, 2019 .
  2. ^ Young art from Baden-Württemberg: focus on the 1990s , art in the VGH, Administrative Court of Baden-Württemberg, accessed on May 3, 2020.
  3. ↑ Oil painting boy . Retrieved May 3, 2020.
  4. ↑ Oliver Schröter: Heise Art Prize: “Young” triggers a sense of home . In: Mitteldeutsche Zeitung , June 3, 2013. Accessed May 5, 2017.
  5. ↑ Frank Weiffen: Colorful adventure trail in the recreation house . In: Leverkusener Anzeiger , January 17, 2014. Accessed May 5, 2017.