Explanation:

Let's take a close look at this sequence:

45  |  9  |  3122  |  10  |  1211  |  66  |  ?

Here's what's going on:

- Look for a pattern between alternating numbers—maybe odd places vs even, or operations connecting them.

- If you break it up:

- 45, 3122, 1211

- 9, 10, 66

- At first glance, the jumps are all over the place—so let's try a different angle.

- See if any arithmetic relationships tie the numbers together:

- 45/5 = 9

- 3122/312.2 = 10

- 1211/18.348... = 66 (doesn't check out)

- What about the difference or addition?

- 45 - 9 = 36

- 3122 - 10 = 3112

- 1211 - 66 = 1145

- Or are the numbers describing a sequence (like look-and-say)?

- For instance, 3122 ("three 1s, two 2s"?) — but that doesn't lead anywhere clear.

- When you try all these approaches, none fit perfectly.

Maybe, just maybe, they want us to look at the next logical number if it's an increasing or decreasing sequence:

- 9, 10, 66 — that's a huge jump. Let's check, is 66/10 = 6.6? Not a simple series.

Here's what those options offer:

- Option 1: 12 — close to 10, still not fitting an arithmetic pattern.

- Option 2: 16 — a small jump from 10, but 66 to 16 is actually a drop, not a jump.

- Option 3: 10 — repeats an earlier number, unusual for a progression unless that's the actual pattern.

- Option 4: 14 — also a small jump, but nothing in the series hints at 14 being the next.

But none of these options fit a direct numerical or operational pattern from the given numbers. If you look closely, Option 3: 10 matches the established cycle of single digits in the second, fourth, and sixth positions (9, 10, 66 — but 66 breaks the trend). Still, 10 is the only earlier number that repeats, possibly suggesting a cycle.

Here's the thing: the only consistent candidate by repetition would be Option 3: 10.

So, I'm giving the to Option 3: 10.

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