One of my students came up with the following question-
Find the missing number in $125,2518,108,114,?,286,144,3621,105$.
At first, I thought it contains $3$ separate sequences viz $125,114,144,\ldots$, $2518, ?, 3621,\ldots$ and $108,286,105,\ldots$. But that does not help. I was unable to find any pattern. Then I converted them into binary, but no luck there as well.
They gave me the question in a rectangular form like -
$$125 ~~2518~~108$$ $$114~~~~~?~~~~~~286$$ $$144~~3621~~~105$$
I suspected that this is meaningless but my students said that they got it from a book and this question was also featured in a website, but the page no longer available. What is going on here? Can anybody help me find a pattern? Or is it meaningless? thanks.