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The following five sequence puzzles are quite nasty and hard to solve. Yet, each of them has a clear and justifiable solution.

Sequence 1:
?, ?, ?, B, B, C, ?, ?, F, ?, S, M, A, S, P, S, C, A, ...

Sequence 2:
?, ?, ?, ?, 8485, 8188, 8167, 8163, 8125, 8091, 8080, 8051, ...

Sequence 3:
..., 23, 4, 16, 33, 21, 6, 18, ?, ?, ?, ?, ...

Sequence 4:
P, M, B, ?, S, C, K, E, L, H, M, H, T, ?, R, ?, ?, ?, S, H, F, B, Y, R, S, D, B, U, M, L, ...

Sequence 5:
1, 2, 6, 7, 6, 5, 0, 6, 0, 0, 2, 2, 8, 2, 2, 9, 4, 0, 1, 4, 9, 6, 7, 0, 3, 2, 0, 5, ?, ?, ?.

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    $\begingroup$ If you like sequence puzzles, you will like the show Only Connect. Example from last week's episode. Only Connect is known for its ruthless difficulty, but it is definitely easier than the sequences here. $\endgroup$
    – Lopsy
    Commented Feb 1, 2015 at 13:35
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    $\begingroup$ Since sequence 4 has been solved last, I count it as the most difficult one of the five sequences. For that reason I assign the "correct answer" sign to Len's answer. $\endgroup$
    – Alexis
    Commented Feb 4, 2015 at 10:40

4 Answers 4

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Sequence 4 is:

the names of the Nobel laureates for Literature - the first letter of their last names listed by year since 1901. The missing letters are shown as follows (X+Y meaning two names in the same year and n/a meaning no award for that year):

P, M, B, M+E, S, C, K, E, L, H, M, H, T, n/a, R, v, G+P, n/a, S, H, F, B, ...

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    $\begingroup$ Len: How did you happen to think of the Nobel prize? $\endgroup$
    – Gamow
    Commented Feb 4, 2015 at 9:38
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    $\begingroup$ @Gerhard - Just luck and perseverance, I guess. I looked at a lot of lists before that. $\endgroup$
    – Len
    Commented Feb 4, 2015 at 18:19
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Sequence 1:

Each letter in this sequence represent the starting letters of the elements of the periodic table arranged on the basis of atomic number

So,the full sequence is

H,H,L,B,B,C,N,O,F,N,S,M,A,S,P,S,C,A,...

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    $\begingroup$ Nasty that Sodium is Na - that threw me. $\endgroup$
    – Floris
    Commented Feb 1, 2015 at 15:38
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    $\begingroup$ @Floris I guess the first sequence was rather nasty. $\endgroup$
    – March Ho
    Commented Feb 1, 2015 at 15:56
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Sequences 2 and 3 can easily be done by googling. For the other three sequences, Google found nothing and I have no idea.

Sequence 2:

Heights of the highest mountains in meters: Mount Everest 8848, K2 8611, Kangchendzonga 8586, Lhotse 8516, Makalu 8485, ... Hence the four questionmarks are 8848, 8611, 8586, 8516.

Sequence 3:

Numbers on a Roulette wheel: 23, 4, 16, 33, 21, 6, 18, 31, 19, 8

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Sequence 5

3, 7 and 6. Those are the last digits of 2^100 = 1267650600228229401496703205376

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