Pretty even fractions

Logic Level 4

\[ \large \square \frac\square\square +\square \frac\square\square = \square \frac\square\square \]

You are given that the numbers \(1,2,3,\ldots,9\) are to be filled into the squares above without repetition such that the equation above shows the sum of two mixed numbers as another mixed number. Find the total possible ways we can arrange these 9 numbers such that this equation holds true.

Details and Assumptions:

  • This is an arithmetic puzzle, where \( 3 \square\square \) would represent the 3-digit number 355 if \( \square = 5 \). It does not represent the algebraic expression \( 3 \times \square \times \square \).

  • A mixed number is the sum a whole number and a proper fraction (stated in lowest form). For example, \( 3\frac56 \) is a mixed number but \(2\frac53\) and \( 3\frac48\) are not mixed numbers.


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