2006 Voluntary Math Challenge

Section 1: Sequence Completion

Below are 28 sequences, each with the last number omitted. Determine the last number in each of the sequences. Little to no outside information is needed to complete the sequences. Each correct answer is worth points equal to its category score. You need not answer every question. Good luck!

Category 1
2, 5, 10, 17, 26, 37, 50, ?
1, 2, 4, 8, 10, 20, 22, 44, 46, ?
0, 1, 3, 6, 10, 15, 21, 28, 36, ?
2, 3, 5, 7, 11, 13, 17, 19, ?
3, 4, 7, 11, 18, 29, 47, 76, ?
1, 6, 2, 8, 5, 12, 10, 18, ?
832, 416, 208, 104, 52, 26, ?

Category 2
1, 2, 4, 7, 12, 20, 33, 54, ?
9, 2, 7, 5, 2, 3, 1, 2, ?
2, 5, 10, 17, 28, 41, 58, ?
1, 2, 6, 24, 120, 720, 5040, ?
33, 25, 17, 9, 1, 7, 1, ?
6, 9, 15, 21, 33, 39, 51, 57, 69, ?
4, 1, 5, 9, 2, 6, 5, 3, 5, 8, ?

Category 3
0, 1, 2, 3, 6, 11, 20, 37, ?
0, 1, 2, 6, 16, 44, 120, 324, ?
100, 141, 173, 200, 224, ?
3, 4, 5, 5, 12, 13, 6, 8, 10, 7, 24, ?
1, 9, 1, 4, 1, 9, 1, 8, 1, 9, 3, 9, 1, 9, 4, ?
1, 4, 4, 2, -2, 1, 6, 9, 3, ?
14, 18, 26, 38, 52, 62, 74, 102, ?

Category 4
155, 19, 8, 5, 4, 4, ?
2, 3, 5, 8, 3, 1, 4, 5, 9, 4, ?
1, 8, 7, 4, 5, 6, 3, 2, 9,
3, 5, 11, 17, 31, 41, 59, 67, ?
1, 2, 4, 10, 34, 154, 874, ?
0, 0, 4, 18, 48, 100, 180, ?
50, 46, 36, 19, 76, 18, ?

Section 2: Grid Puzzles

Below are 28 grids of Xs and Os. Some of the positions on the grids have been replaced by question marks (?). Identify the identity of each question mark (X or O) in the following grids. Click on a question mark to change it. There is no "partial credit" for identifying only certain grid positions.

Category 1

Category 2

Category 3

Category 4

Section 3: Your Information

If your score is sufficiently high, you will be inducted into the Hall of Fame. To let everyone know your incredible mathematical prowess, please enter your name into the field below. We will not use your name for any other purposes.

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