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 Basic knowledge (Posted on 2006-01-10)
What is the next number in this sequence?

10, 20, 120, 440, 3200, 20460, 116600, 612700...

What is the general rule behind the sequence?

Hint: This sequence starts in n=2. A computer will probably not be able to solve it, but you're welcome to try.

 Submitted by Alexis Rating: 5.0000 (1 votes) Solution: (Hide) The next number in the sequence is 3628800. The general rule behind the sequence is to write n! in base n. For the first number, 2!=2, written in base 2 (binary) is 10. For the second number, 3!=6, written in base 3 would be 20 (2*3^1 + 0*3^0). For the third number, 4!=24, written in base 4 would be 120 (1*4^2 + 2*4^1 + 0*4^0). For the last number (the ninth number), 10!=3628800, which written in base 10 is the same number. Therefore, the answer is 3628800, or 10!. If anyone wants to try with a computer, please post the solution you find. I think it would be interesting to see how a computer simulates human intuition.

 Subject Author Date Solution To Part II K Sengupta 2008-04-18 15:58:14 Solution To Part I K Sengupta 2008-04-18 15:50:02 Yep Justin 2006-03-17 19:26:34 Solution The riddler 2006-01-11 22:59:37 Hint goFish 2006-01-11 10:12:22

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