5
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The puzzle asks to determine the next term in the sequence 2, 4, 8, 0, 0, 16...

a. 32
b. 18
c. 20
d. 24
e. 0

The obvious answer for me would be 32, with these zeros serving as the "neutral element" of the sequence. But I feel uncomfortable because it's almost like discarding them to produce a sequence like 2, 4, 8, 0, 0, 16, 32, 64, 0, 0, 128, 256, ...

Is there some closed formula or logic to determine the next term? Maybe an = 0, n mod 5 = 0?

(Source (pg. 182))

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    $\begingroup$ What does the title refer to? Does the puzzle ask to modify 2n^2 to get 2, 4, 8, 0, 0, 16... that continues to one of a.-e. answers? $\endgroup$
    – Vepir
    Jan 1, 2021 at 18:04
  • $\begingroup$ I feel like the question needs more information/context to be answerable. I agree the pattern of numbers/gaps could be 3-2-3-2..., but I was more interested in the fact the numbers could be decreasing: we only get 3-2-1. So maybe the pattern is 3-2-1-3-2-1... Or maybe something else entirely! It's not really clear (at least to me) $\endgroup$
    – Helen
    Jan 1, 2021 at 23:15
  • $\begingroup$ Without looking at the source,this could also be a linear recurrence $a_{n+3}=2 a_n - a_{n+1}$. Then the next number would be $0$. $\endgroup$
    – WimC
    Jan 2, 2021 at 8:40
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    $\begingroup$ It seems the answer is not given in your book. This is not a book dedicated to puzzles but to data communication and information security. This puzzle must be related to the chapter it belongs to. What is that chapter about? $\endgroup$
    – xhienne
    Feb 1, 2021 at 20:51

1 Answer 1

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I think the answer is

0

Reasoning

For $n \geq 3$, the numbers seem to follow the recursive relationship $$a_{n} = 16 - a_{n-1} - 2a_{n-2}$$ In particular, $$8 = 16 - 4 - (2\times 2) $$ $$0 = 16 - 8 - (2\times 4) $$ $$0 = 16 - 0 - (2\times 8) $$ $$16 = 16 - 0 - (2\times 0) $$ and finally $$0 = 16 - 16 - (2\times 0) $$

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