If all 720 permutations of 123456 are put in numerical order, what is the 407th pemutation?

Here's how I would do it.

The 1-120 permutations begin with 1,
The 121-240 permutations begin with 2,
The 241-360 permutations begin with 3,
The 361-480 permutations begin with 4,
The 481-600 permutations begin with 5,
The 601-720 permutations begin with 6,

So the 407 permutation must begin with 4.

The 361-384 permutations begin with 41
The 385-408 permutations begin with 42
The 409-432 permutations begin with 43
The 433-456 permutations begin with 45
The 457-480 permutations begin with 46

So the 407 permutation begins with 42.

You could continue this method to find the answer. I think an easier way is seeing the last permutation (numerically) that begins with 42 is the 408 permutation, which is 426531; the digits after 42 are highest to lowest. So the 407 term must be 426513

Posted by Gamer on 2003-07-23 11:28:56