# Intelligent Math Puzzle – Challenge 86

This math puzzle does not require any special mathematical knowledge, just logical reasoning and creative thinking.

## Challenge:

If $$\frac{1}{3} = \frac{1}{\triangle} + \frac{1}{\triangledown}$$ what is the value of $$\triangledown × \triangle$$ ?

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$$\triangledown$$ and $$\triangle$$ are two digits. The sum of two fractions $$\frac{1}{\triangle}$$ and $$\frac{1}{\triangle}$$ equals to $$\frac{1}{3}$$. Obviously, there are many values for $$\triangledown$$ and $$\triangle$$ that can be used in the equation.
Choose a value for $$\triangledown$$. Let’s put 4 for $$\triangledown$$. Then:
$$\frac{1}{3} = \frac{1}{\triangle} + \frac{1}{4} →\frac{1}{3} – \frac{1}{4} = \frac{1}{\triangle} → \frac{4}{12} – \frac{3}{2} = \frac{1}{\triangle} → \frac{1}{12} = \frac{1}{\triangle} →\triangle = 12$$
Therefore: $$\triangledown × \triangle = 4 × 12 = 48$$