# Magic triangle (mathematics)

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A magic triangle (also called a perimeter magic triangle [1] ) is an arrangement of the integers from 1 to n on the sides of a triangle with the same number of integers on each side, called the order of the triangle, so that the sum of integers on each side is a constant, the magic sum of the triangle. [1] [2] [3] [4] Unlike magic squares, there are different magic sums for magic triangles of the same order. [1] Any magic triangle has a complementary triangle obtained by replacing each integer x in the triangle with 1 + nx. [1]

## Examples

Order-3 magic triangles are the simplest (except for trivial magic triangles of order 1). [1]

## Related Research Articles

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Number Scrabble is a mathematical game where players take turns to select numbers from 1 to 9 without repeating any numbers previously used, and the first player with a sum of exactly 15 using any three of his number selections wins the game. The game is isomorphic to tic-tac-toe, as can be seen if the game is mapped onto a magic square.

A magic polygon is a polygonal magic graph with integers on its vertices.

## References

1. "Perimeter Magic Triangles". www.magic-squares.net. Retrieved 2016-12-27.
2. "Perimeter Maghic Polygons". www.trottermath.net. Retrieved 2016-12-27.
3. "Magic Triangle : nrich.maths.org". nrich.maths.org. Retrieved 2016-12-27.
4. "P4W8: Magic Triangles and Other Figures" (PDF). Retrieved December 27, 2016.