Looking at the Puzzling Stack Exchange recently, I found a surfeit of number sequence riddles that all look the same! I mean, there's no difference between any of them. I'm sick and tired of all these uninspired riddlers cluttering up our precious site with all of their garbage!
Well anyhoo, what comes next?
0 0 1 3 4 5 5 5 6 6 8 9 11
0 2 3 3 6 7 10 11 14 17 17 18 19
0 0 1 1 2 3 4 5 6 7 7 8 9
0 3 4 4 8 8 8 9 11 11 11 14
Hint:
Before you consider my riddle to shelve,
know that its message has characters twelve.
Hint 2:
Maybe it's the math, which you are missing,
CRT you should not be dismissing.
Answer
The next number is:
14
We can namely do the following:
If for each line we take the difference between all pairs of consecutive integers, we get the following:
0 1 2 1 1 0 0 1 0 2 1 2
2 1 0 3 1 3 1 3 3 0 1 1
0 1 0 1 1 1 1 1 1 0 1 1
3 1 0 4 0 0 1 2 0 0 3
The second hint refers to the Chinese remainder theorem, which seems to mean that these four sequences are actually the same sequence, just modulo different numbers. These moduli appear to be 3, 4, 2 and 5 respectively, resulting in the following sequence modulo 60:
18 1 20 19 25 15 21 7 15 20 13, and some number that is 5 mod 12.
Replacing these numbers by letters (1 -> A, 2 -> B, etc.), we get the message RATSYOUGOTM?, where the ? is either an E or a Q (corresponding to either 5 or 17). This should be an E, so the last number is 5. From this we see that the last difference should be 0, and the last number of the riddle is 14.
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