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 , … , 9 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 □ □ 3 \square\square would represent the 3-digit number 355 if □ = 5 \square = 5 . It does not represent the algebraic expression 3 × □ × □ 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 5 6 3\frac56 is a mixed number but 2 5 3 2\frac53 and 3 4 8 3\frac48 are not mixed numbers.

8 0 4 16 32

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Pi Han Goh by Pi Han Goh , 30, Malaysia

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2 solutions

Gustavo Cardenas
Aug 13, 2015

In order to have different numbers in each square, the first two denominators should be relatively prime and the result denominator should be their product. The only numbers between 1 and 9 that match that rule are 2, 3 and 6, so the fraction part of the LHS should be 1 2 \frac{1}{2} and 1 3 \frac{1}{3} or 2 3 \frac{2}{3} , but for that we need to repeat some numbers, which is against the rules of the problem.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

you can not use any numbers to be the lower part of the proper fraction

0 Helpful 0 Interesting 0 Brilliant 1 Confused

what do u mean?

Pi Han Goh - 5 years, 10 months ago

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