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Basic knowledge (Posted on 2006-01-10) Difficulty: 4 of 5
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.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionSolution To Part IIK Sengupta2008-04-18 15:58:14
Some ThoughtsSolution To Part IK Sengupta2008-04-18 15:50:02
YepJustin2006-03-17 19:26:34
Hints/TipsSolutionThe riddler2006-01-11 22:59:37
HintgoFish2006-01-11 10:12:22
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