Teaser 5

What is the next digit in this sequence?

   1, 1, 1, 1, 5, 1, 7, 2, 3, 5

Hint

There's a corresponding sequence: 12, 6, 4, 3, 12, 2, 12, 3, 4, 6

Answer

   11

Explanation

Start with 1/12 (one-twelfth), and then keep adding 1/12. You end up with the sequence 1/12, 2/12, 3/12, 4/12, …. Next reduce each term to its simplest form. This results in: 1/12, 1/6, 1/4, 1/3, 5/12, 1/2, 7/12, …. The numerators from these fractions give you the original sequence.