Following are several sets of numbers based on particular (and different) patterns (though not necessarily mathematical patterns), arranged from least difficult to most difficult, and with corresponding point values. The maximum score is 100 - how high can you get? If your answer doesn't match the one I submitted, but makes sense, you may credit yourself the points.
(1):(2 points):(3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, 6, 8, ?)
(2):(4 points):(1888, 1892, 1896, 1904, ?)
(3):(5 points):(1, 12, 1, 1, 1, 2, ?)
(4):(6 points):(0, 1, 256, 2187, 4096, 3125, 1296, ?, 64, 9, 1)
(5):(9 points):(1, 22, 12, 5, 26, 16, 7, 28, 18, ?)
(6):(12 points):(2, 4, 5, 6, 9, ?, 15, 21, 26)
(7):(15 points):(0, 4, 7, 0, 2, 4, 6, 8, 0, 1, 3, 4, ?)
(8):(21 points):(6, 10, 14, 15, 21, 22, 26, 33, 34, 35, ?)
(9):(26 points):(0.4330, 1.0000, 1.7205, 2.5981, 3.6339, 4.8284, 6.1818, ?)
I thought of (3) as a calendar, not a clock, but it's much the same as DJ's answer. Pairing the numbers off, we get 1/12, 1/1, 1/2, or December first, January first, February first, so to continue we would have March first, 1/3, the next two numbers in the series being 1 and 3. It just occurred to me that this doesn't work in the US, where dates are usually written the other way round.
Alternative solution: We could read the numbers as months, giving us January, December, Jan., Jan., Jan., February. Then the sequence is obviously the first month in which it snowed on Mount Pooka-Pooka in consecutive winters, beginning with the winter of 1837/8 and up to 1842/3. Unfortunately, the next in the series refers to the infamously warm dry winter of 1843/4, when it didn't snow at all. Just kidding. Sorry.
sequence 3
