Mazarae
A Mazarae is a kind of mathematical puzzle based on the idea of a magic square.
| Author | Hanspeter Leupp |
|---|---|
| Country | Switzerland |
| Genre | riddle, mind sport |
| Publisher | Thaynger Anzeiger and Neuhauser Woche |
| Published | 2015 |
| Website | www |
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History
Mazarae was developed by Hanspeter Leupp[1] in Schaffhausen, Switzerland. These "magic number riddles" (coming from the German word "Magisches Zahlenrätsel" or Mazarä [2]) were published for the first time in the year 2015 in form of a contest in the Swiss newspaper Thaynger Anzeiger.[3] Leupp's riddle was surprisingly successful and a large number of readers participated in the contest. Since this success, the riddle is taking place monthly in two newspapers called Thaynger Anzeiger and Neuhauser Woche.
Characteristics
A Mazarae puzzle consists of a magic square with certain numbers removed. The challenge for the solver is to reconstitute those missing numbers. The puzzle may be played on a 3×3, 4×4, or larger grid. The conditions of a Mazarae are that all rows and columns as well as both diagonals have to add up to a specified sum, that no number can occur twice, and that only whole numbers (1, 2, 3, …) are to be used.
Further conditions can apply to a Mazarae puzzle. For example, the numbers to be used can be limited, or a further internal grid can be added to the original grid, etc. The difficulty of the riddle depends on the location of the removed numbers.
Examples and solutions
1. An example for a Mazarae is the following 4×4 grid, partially filled in:
Sum 90 6 15 22 9 28 34 35 12
1. The solution to this Mazarae is the following completed grid:
6 47 15 22 9 28 24 29 34 3 35 18 41 12 16 21
2. Example: (difficult)
Sum 112 4 35 19 25 17 31 13
2. Solution: (difficult)
4 35 54 19 48 25 22 17 31 42 23 16 29 10 13 60
3. Example with 5×5 grid:
Sum 135 23 2 27 17 14 39 43 37 29 26 49 8 16 35
3. Solution for 5x5 grid:
28 55 23 2 27 17 14 39 22 43 33 10 37 29 26 49 41 20 21 4 8 15 16 61 35
See also
References
- ↑ Leupp (born in the year 1934). He participated and won the contest Euler: http://euler-2007.ch/wettbewerb/loesung4.pdf.
- ↑ www
.mazarae .ch. - ↑ http://www.thayngeranzeiger.ch/ (newspaper of the canton Thayngen).
- http://www.mathematische-basteleien.de/magquadrat.htm
- http://www.mathe-online.at/materialien/maria.koth/files/Magische_Quadrate_Infotext.pdf
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