Here is what we have:
1/7 = 0.142857... 1/11 = 0.090909... 1/13 = 0.076923...
Notice that if you add the first three digits to the next three digits, you always get 999:
142 + 857 = 999 090 + 909 = 999 076 + 923 = 999
Oddly, the same thing happens with
2/13, and so on, as the numerator increases: adding the first three digits to the next three digit results in 999.
OK. Multiplying the denominators 7 x 11 x 13 results in 1001.
What is the relationship between the fraction series
x/7, x/11, x/13, and the result of multiplying the denominators?
(This is taken from an example in the book "Ten Ways to Destroy the Imagination of Your Child" by Anthony Esolen. The examples above are presented separately, and the reader is encouraged to be imaginative in discovering how they are related. After almost 20 years of playing math/CS games, I suppose I still have no imagination to solve this kind of thing.)