# Math puzzle

A math puzzle is a math- based puzzle . The mathematical facts often come from number theory or geometry .

A famous inventor of such puzzles was the American Samuel Loyd (1841–1911), who from 1870 published his puzzles in numerous newspaper columns and magazines. The player inventor Martin Gardner (1914-2010) also invented and published numerous new math puzzles. Usually such tasks are packed into a little anecdote with an exciting title so that they don't have to be explained too dryly in mathematical terms.

Various magazines, including Die Zeit , regularly publish math puzzles for the entertainment of their readers. A new type of mathematical puzzles are puzzles like Sudoku , which were made famous worldwide by the Japanese magazine Nikoli .

## Types of puzzles

### Geometric puzzle

Example: A farmer wants to tie up a cow in the meadow in such a way that it can eat exactly one semicircle. However, he only has three stakes and two long ropes available. How does he have to tie up the cow?

### Number theory puzzle

Example: The children of a village school are asked to stand in rows of three in the school yard. Since there are two children left, the teacher orders them to stand in rows of four. Again two children are left and the teacher orders them to stand in rows of five. Now it is opening. How many children are in school?

### Logical puzzle

Example: Martin and Manfred are identical twins. One of them always lies, the other always tells the truth. You now meet exactly one of the two.

1. What question do you have to ask to find out which of the two is the liar?
2. What question do you have to ask to find out which of the two twins you have in front of you?

The logician Raymond Smullyan is a master at writing this type of puzzle and has published several puzzle books. The so-called zebra puzzle (also known as Einstein's puzzle ) occupied the British and American readership of a magazine for months in 1963.

### Symbol puzzles and alphametics

A special form of the mathematical puzzle is the symbol puzzle or alphametics, in which the aim is to reconstruct an equation in which the digits have been replaced by symbols or letters. Usually, each digit is represented by only one symbol, and the first symbol of a number cannot stand for 0.

A symbol puzzle could look like this:

```ACE + DAC = JFD
-     +     -
AAA - HFC =  GI
=     =     =
AH + III = JBJ
```

The letters must be replaced by numbers in such a way that all equations are fulfilled horizontally and vertically. Alphametics can also be entertaining if the letters also form words. Probably the best known example of this is

```  SEND
+ MORE
------
MONEY
```

which, according to legend, was sent by a student to his father. The question now is how much "MONEY" is.

There are also such alphametics in German. Here is a multiplicative, especially for Wikipedia:

```ESSAY * WERK = WIKIPEDIA
```

Multiplicative alphametics are often supplied with the written multiplication as well, to make the solution easier; occasionally, so that it is clear at all:

```ESSAY * WERK
------------
KPYPIY
RSERPY
WIWKPA
YYISIA
------------
WIKIPEDIA
```

### Arithmetic puzzle

Example for children: 5 numbers between 1 and 9 are linked using the basic arithmetic operations , whereby the result and, depending on the level of difficulty, a different number of numbers are given in changing patterns. The numbers to be inserted (framed fields) must not appear twice. The result and the individual subtotals are always whole numbers and positive. The example is suitable for students from the 2nd grade. See also Miss Lupun .

Example for adults: The same puzzle principle is increased to 9 numbers, but point calculation does not apply before line calculation . Logic can be used to limit the number of possible combinations (what subtotals are divisible by the number X?), But the focus of these puzzles is on mental arithmetic.

Another well-known arithmetic puzzle is the “ four fours ” puzzle , in which the aim is to represent given numbers with four fours.

## literature

• Sam Loyd , Martin Gardner (Ed.): Mathematical puzzles and games . 3rd edition DuMont, Cologne 2004, ISBN 3-8321-7359-5
• Raymond Smullyan: What is this book (English. What is the name of this book ). Vieweg, Braunschweig and Wiesbaden 1981, ISBN 3-528-08436-7
• Raymond Smullyan: Alice in the Rätselland (English Alice in the Puzzle Land ). 2nd edition Fischer, Frankfurt am Main 1989, ISBN 3-596-28701-4
• Raymond Smullyan: Lady or Tiger (Engl. The Lady or the Tiger ). 3rd edition Fischer, Frankfurt am Main 1987, ISBN 3-596-28176-8
• Raymond Smullyan: Mockingbirds and other meta birds (English To Mock a Mockingbird ). Fischer, Frankfurt am Main 1989, ISBN 3-596-28712-X
• Raymond Smullyan: Logic Knights and Other Villains (English Forever undecided. A puzzle Guide to Gödel ). Fischer, Frankfurt am Main 1991, ISBN 3-596-10349-5
• Raymond Smullyan: Satan, Cantor and Infinity , Insel, Frankfurt am Main 1997, ISBN 3-458-33599-4