Using The Yul Brynner Theorem (or Vin Diesel Theorem)
Note: These number series were taken from a practice test for a Computer Programmer's Aptitude Exam. Given the initial series of numbers which follow some logical order, you need to select "next number" from the five choices AD....and document your reasoning.
 1 2 4 3 5 9 __ : A(4) B(5) C(6) D(7) E(8)
 5 10 15 3 8 __ : A(2) B(4) C(13) D(18) E(20)
 3 6 8 9 12 __ : A(4) B(8) C(11) D(14) E(16)
 1 2 3 5 7 9 12 __ : A(15) B(16) C(17) D(18) E(19)
 4 9 5 7 6 5 7 __ : A(3) B(4) C(7) D(8) E(9)
 2 4 12 3 15 __ : A(4) B(5) C(12) D(18) E(21)
 9 8 7 6 8 10 __ : A(4) B(7) C(12) D(14) E(16)
 15 20 4 20 15 __ : A(4) B(10) C(16) D(20) E(25)
 2 4 8 3 6 12 4 __ : A(2) B(4) C(6) D(8) E(16)
 3 1 4 2 5 3 __ : A(2) B(4) C(6) D(8) E(10)
Note: Why include these sequences as interesting problems? And why the picture of Yul Brynner above?
Because statisticians for psychological testing agencies have proven that any of the five choices can be proven to be a "correct" answer. In fact, e or pi could be the "correct" answer for all ten problems!
Using the principles of curve fitting, the key idea is informally called the Yul Brynner Theorem (or the Vin Diesel Theorem for the younger crowd). If you want to know more about this (and why number sequences rarely show up on aptitude exams any more, consider reading
this paper.
Source: Adapted from John Jensen's How To Pass Computer Programmer Aptitude Tests, 1967
Hint: Consider the first one...see the pattern +1, +2, 2, +3, +4, 4...or the missing next number is B(5).
Now, this clue may frustrate you...but that is the type of logic used by the creator of the sequences.
Solution Commentary: The "given answers" used these sequences:
 +1, +2, 2, +3, +4, 4...
 +5, +5, ÷5, +5, +5...
 +3, +2, +1, +3, +2...
 +1, +1, +2, +2, +2, +3 +3...
 +1 (between odd numbered terms and 2 (between even numbered terms)...
 +2, x3, ÷4, x5, +6...
 1, 1, 1, +2, +2, +2...
 +5, ÷5, x5, 5, +5...
 x2, x2, +1 (1st & 4th terms), x2, x2, +1 (4th & 7th terms), x2...
 2, +3, 2, +3, 2, +3...
Note: Don't get angry at me...these were written by the author of the practice exam.
Also, could you use the ideas in the suggested paper to show how any of the available choices for a number sequence could be "correct"?
