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The strategy becomes much more interesting when you realize that guessing math games randomly is inefficient.

A smart player can use the midpoint strategy. Instead of guessing 1, then 2, then 3, you might guess 50 first. If the answer is lower, you immediately eliminate half of the possible numbers.

This simple game introduces an important mathematical idea: reducing possibilities as efficiently as possible. 

Magic squares are among the most fascinating mathematical puzzles ever created. In a traditional magic square, numbers are arranged in a grid so that every row, column, and sometimes diagonal has the same total.

For example, the classic 3-by-3 magic square uses the numbers 1 through 9. Each row, column, and main diagonal adds up to 15.

At first, arranging the numbers correctly can seem almost impossible. But once you understand the underlying patterns, the puzzle becomes much more manageable.

Magic squares are a great example of how mathematics can produce structures that look almost magical while being completely logical.