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Given this equation:

$$ \frac{(n - 10)(n - 9)(n - 8)\times\ldots\times(n - 2)(n - 1)n}{11!} = 12376 $$

How would I find $n$?

I already know the answer to this, all thanks toWolfram|Alpha, but just knowing the answer isn't good enough for me. I want to know on how I would go about figuring out the answer without having to multiply each term, then using algebra to figure out the answer.

I was hoping that there might be a more clever way of doing this.

  • 2
    Why not? Brute forcing is very effective, when you can count the number of values that you need to test with your fingers, as is the case here. If you can factor 12376, you will get a very good starting point, but that is a coincidence. Also, if your book has a largish part of Pascal's triangle printed out...2011-09-27

7 Answers 7