Ten fractions

Level 2

Is it possible to write 10 fractions using the first 20 integers, so that their sum is a whole number?

No . Yes It's impossible to know

Gonzalo Píngaro by Gonzalo Píngaro , 45, Argentina

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1 solution

Gonzalo Píngaro
Sep 10, 2018

One possible way is: 19 8 + 17 4 + 13 2 + 14 16 + 9 15 + 7 5 + 18 6 + 12 3 + 11 1 + 20 10 = 36 \frac{19}{8}+\frac{17}{4}+\frac{13}{2}+\frac{14}{16}+\frac{9}{15}+\frac{7}{5}+\frac{18}{6}+\frac{12}{3}+\frac{11}{1}+\frac{20}{10}=36

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Interesting problem. How did you think of this solution?

X X - 2 years, 9 months ago

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Well... first of all I assigned large prime numbers to a power of two, and I set 19/8+17/4+13/2+x/16=n \in N for some x. Then, I set the 11/1 for 11 is a prime number I then is done!

Gonzalo Píngaro - 2 years, 7 months ago

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