Advent Puzzles 2014: puzzle 17 solution

Advent puzzle 17: 1/a + 1/b + 1/c + 1/d + 1/e + 1/f = 17/12. Given 1<a<b<c<d<e<f<17 find a, b, c, d, e and f.

— Portsmouth MathsJam (@MathsJamPOR) December 17, 2014

$\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}=\frac{17}{12}$

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