Can you Make it One-third?

Number Theory Level 4

Can you arrange the numerals 1 to 9 (1, 2, 3, 4, 5, 6, 7, 8 and 9) in a single fraction that equals exactly 1/3 (one third)? If So,what is the sum of digits in its Numerator?


The answer is 18.

Dhinesh Ganesan by Dhinesh Ganesan , 25, India

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2 solutions

Dhinesh Ganesan
Jul 14, 2014

THE POSSIBLE FRACTIONS ARE 5832/17496 = 1/3

5823/17469 = 1/3

5+8+3+2=18 .

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How did you arrive at that fraction?Please explain clearly!

Anik Mandal - 6 years, 10 months ago

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Trial and Error Method :p

Dhinesh Ganesan - 6 years, 10 months ago

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Is there no other way to solve it? @Dhinesh Ganesan

Anik Mandal - 6 years, 9 months ago

ooh, tricky problem, this one, being that there are 2 such fractions

Michael Mendrin - 6 years, 11 months ago

do we have any other method to solve it ?

Sriram Venkatesan - 6 years ago
Chew-Seong Cheong
Sep 11, 2014

There are two possible fractions:

5823 17469 = 5832 17496 = 1 3 \dfrac{5823}{17469} = \dfrac{5832}{17496} = \dfrac{1}{3}

Both numerators have the same digits and their sum = 2 + 3 + 5 + 8 = 18 2+3+5+8 = \boxed{18}

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