# Finish The Pattern #3 [closed]

Given this pattern:

0, 1, 0, 2, 2, 2, 3, 4, 5, 6, 6, $n$

Find the next item at $n$

Pattern/sequence explanation required

## closed as too broad by mdc32, xnor, leoll2, Engineer Toast, Aggie KiddMay 4 '15 at 13:56

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• -1. These puzzles seem to be completely random and have multiple solutions. Even the "right" answer seems no more logical than a polynomial created to fit the data. – mdc32 May 3 '15 at 5:15

12

Because...

If you were to group all numbers in batches of 3, add them up and then get the average between them (rounding up), you get a sequence of it's own which goes 1(?) 2 3 4. Done as follows:
0 1 0 = ? (I'm assuming 1)
2 2 2 = 6 / 3 = 2
3 4 5 = 12 / 3 = 4
6 6 12 = 24 / 3 = 8

I'm probably horrible mistaken, but I thought I'd give it a shot.

• Correct! And (0 + 1 + 0) / 3) should be rounded to 1 (as you said). It should be noted that it was the ceiling average (all decimals round up). – Zach Gates May 3 '15 at 4:05
• @ZachGates No way... I'm kind of amazed actually. I'm bad at puzzles haha. The reason I put one to begin with was if the averages would be a sequence, 0, 2, 4, 8 wouldn't make any sense. Which is why I assumed 1. – MisterBla May 3 '15 at 4:08

I feel like there may be multiple solutions to this puzzle, but I'll propose one I found.

The next number is:

6

Because

Each group of three adds up to a multiple of 6, alternating between consecutive integers and the same 3 digits repeated.