# Numbers

Numbers are an important element of mathematics. In this section, we are going to investigate numbers in a ．number・ of ways. We will investigate some ．number puzzles・, in which certain digits have been left out or coded, and we had to work them out. There will also be other interesting issues regarding the properties of numbers.

### Completing Calculations

．Completing Calculations・ are mathematical problems in which digits in a calculation have been replaced by alphabets, such that each alphabet corresponds uniquely to one digit. Our task is to work out those missing numbers. Very often, a small observation is crucial to solving the entire problem. Common ．observations・ include carry digits, divisibility, etc. Here we will discuss a few examples, after which there are several challenges for the readers.

### For 'lonely':

Here we will present nine further puzzles. In the first one, all the digits in the entire calculation is missing, except a digit ．1・; in the second one, a digit ．2・, and so on, and in the last one, a digit ．9・.

#### Magic Squares/Polygons

Magic squares have often been regarded as one of the most ．beautiful・ products in mathematics. In this section, we will give a brief account of how magic squares can be worked out. We will also examine a variation of magic square, in which the square shape had been changed to some other shapes. We call them ．magic polygons・.

#### Other TopicsThe Beauty of NumbersDecimal

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