For what it's worth, the problem (and a related one) was posed in the *American Mathematical Monthly*, 1910 [(vol. 17, no. 6/7, pg. 150)][1] and a solution given in 1911 [(vol. 18, no. 2, pp. 41-43)][2].

[1]: http://www.jstor.org/stable/i349281
[2]: http://www.jstor.org/stable/2973946