MAGIC SHAPES

1. MAGIC SQUARES

There are different magic shapes, but the most popular is a square. If you add numbers placed in its fields in every row, column, and both diagonals, the sums will be equal. Here are some examples:

19 26 21
24 22 20
23 18 25
1 35 34 4
32 6 7 29
8 30 31 5
33 3 2 36

Try to fill out squares with numbers given next to them. Then click on check to see how many you got right.


2. MAGIC SQUARES WITH BORDERS

An advanced form of a magic square is a magic square with a border. The square actually consists of two magic squares. One is bigger and has a smaller one in the middle. In order to understand this type of square, it is best to look at an example.

9 25 26 23 18 10
16 1 35 34 4 21
20 32 6 7 29 17
24 8 30 31 5 13
15 33 3 2 36 22
27 12 11 14 19 28

Try to build a square 1-3-5-7 filled with numbers 1-49.

3. MAGIC TRIANGLES

A magic triangle has equal sums of numbers on its sides. A triangle is magical in two ways—both the sum of the numbers on its sides are equal, and the sum of squares of those numbers is also equal.

Try to build other shapes..