# 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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The correct answer is 48.

\(\triangledown\) 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: \(\triangledown × \triangle = 4 × 12 = 48\)

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