General Mathematics

Core Theoretical Principles

This subject explores mathematical puzzles, mental calculation methods, and universal principles that span multiple disciplines.

1. Magic Squares ($4 \times 4$)

A magic square of order $n$ is an $n \times n$ grid of distinct positive integers such that the sum of the numbers in each row, column, and main diagonal is constant:

$$ M = \frac{n(n^2 + 1)}{2} $$

For an order $n = 4$ square containing integers $1, 2, \dots, 16$, the magic constant is:

$$ M = \frac{4(16 + 1)}{2} = 34 $$

Watch our step-by-step video lecture to master the 30-second magic box trick and understand the underlying modular symmetry.