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, ?)

Here are some more that I figured out, or at least that I think I can explain. I've included the answers other people have come up with:

1. The number of letters in each counting letter:
   one(3), two(3), three(5), four(4), five(4), six(3), seven(5), eight(5), nine(4), ten(3), eleven(6), twelve(6), thirteen(8), fourteen(8), fifteen(7) ...
   ? = 8
   


2. Consecutive leap years, starting in 1888:
   1888, 1892, 1896, 1904, 1908, 1912 ...
   ? = 1908


3. It looks like every other term in this one is a 1, and the other terms are in a 'clock' (mod 12) counting order. The given sequence isn't long enough to adequately verify this, but here goes:
   1, 12, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5 ...
   ? = 1


4. S_n=n^(10-n):
   0=0^10, 1=1^9, 256=2^8, 2187=3^7, 4096=4^6, 3125=5^5, 1296=6^4, 343=7^3, 64=8^2, 9=9^1, 1=10^0
   ? = 343


5. The dates of every third Wednesday of this year (or the date every third week, starting with January first in a non-leap year):
   Jan 1, Jan 22, Feb 12, Mar 5, Mar 26, Apr 16, May 7, May 28, Jun 18, Jul 9, Jul 30 ...
   ? = 9


6. These numbers are the point values assigned the problems in this quiz! This one had me going for so long..
   2, 4, 5, 6, 9, 12, 15, 21, 26
   ? = 12


7. S_n is the tenth spot (first decimal place) in √n:
   √1=1.000, √2=1.414, √3=1.732, √4=2.000, √5=2.236, √6=2.449, √7=2.645, √8=2.828, √9=3.000, √10=3.162, √11=3.316, √12=3.464, √13=3.605, √14=3.741
   ? = 6


8. This is the sequence of all numbers with exactly two different prime factors, arranged in ascending order:
   6=2×3, 10=2×5, 14=2×7, 15=3×5, 21=3×7, 22=2×11, 26=2×13, 33=3×11, 34=2×17, 35=5×7, 38=2×19, 39=3×13 ...
   ? = 38


9. I still have no clue for this one. Incidentally, .4330 is (√3)/4, 2.5981 is (3√3)/2, but I have no idea if that's where those would come from, or what they mean.

Overall, I think I myself completely solved numbers 1, 2, 4, and 6.
My answer to number three is iffy, and probably not the intended solution, but I'm taking it.
For number five, I noticed that that the difference between both pairs of ascending terms was the same, 21, and I guessed it was some sort of mod scale. I got different values, though; some 30, some 31, and the second one even came out to 28! .. If I had been awake that would have been easy. Anyway, I corrected Bryans answer (three weeks from June 18 is July 9, not 13), so I'm claiming those points as well.
Number seven I would have gotten in a few weeks, or years. I'll relinquish those points.
For the values in number 8, I had noticed that each had exactly two different prime factors, but I was thinking too much. I mulled over the order, trying to find a pattern, and missed the simple ascension of the results. I would take only half of those points, but 21 doesn't divide by two very evenly, so I'll just take them all.
I didn't get the last one, and no one else has yet either.

Total: 2 + 4 + 5 + 6 + 9 + 12 + 21 = 59.
Looks like I still failed..
Actually, for number seven, I did notice that the postions of the zeroes (1, 4, 9) were the perfect squares. So, that would eventually have led to me listing the square roots of the numbers, and making the same observation that fwaff did. It's not my fault he blurted out the answer before I had the chance! So, I deserve those points too.

My total score then is: 2 + 4 + 5 + 6 + 9 + 12 + 15 + 21 = 74.
And hey, I only missed the last sequence. Too bad you guys each only got one or two ...

=P

Posted by DJ on 2003-08-01 03:10:00