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# All the 720 arrangements of the digits 1 through 6 are put in numerical order. What is the 428th term?

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All the 720 arrangements of the digits 1 through 6 are put in numerical order. What is the 428th term?

Feb 3, 2018

#1
+1

{{1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 6, 5}, {1, 2, 3, 5, 4, 6}, {1, 2, 3, 5, 6, 4}, {1, 2, 3, 6, 4, 5}, {1, 2, 3, 6, 5, 4}, {1, 2, 4, 3, 5, 6}, {1, 2, 4, 3, 6, 5}, {1, 2, 4, 5, 3, 6}, {1, 2, 4, 5, 6, 3}, {1, 2, 4, 6, 3, 5}, {1, 2, 4, 6, 5, 3}, {1, 2, 5, 3, 4, 6}, {1, 2, 5, 3, 6, 4}, {1, 2, 5, 4, 3, 6}, {1, 2, 5, 4, 6, 3}, {1, 2, 5, 6, 3, 4}, {1, 2, 5, 6, 4, 3}, {1, 2, 6, 3, 4, 5}, {1, 2, 6, 3, 5, 4}, {1, 2, 6, 4, 3, 5}, {1, 2, 6, 4, 5, 3}, {1, 2, 6, 5, 3, 4}, {1, 2, 6, 5, 4, 3}, {1, 3, 2, 4, 5, 6}, {1, 3, 2, 4, 6, 5}, {1, 3, 2, 5, 4, 6}, {1, 3, 2, 5, 6, 4}, {1, 3, 2, 6, 4, 5}, {1, 3, 2, 6, 5, 4}, {1, 3, 4, 2, 5, 6}, {1, 3, 4, 2, 6, 5}, {1, 3, 4, 5, 2, 6}, {1, 3, 4, 5, 6, 2}, {1, 3, 4, 6, 2, 5}, {1, 3, 4, 6, 5, 2}, {1, 3, 5, 2, 4, 6}, {1, 3, 5, 2, 6, 4}, {1, 3, 5, 4, 2, 6}, {1, 3, 5, 4, 6, 2}, {1, 3, 5, 6, 2, 4}, {1, 3, 5, 6, 4, 2}, {1, 3, 6, 2, 4, 5}, {1, 3, 6, 2, 5, 4}, {1, 3, 6, 4, 2, 5}, {1, 3, 6, 4, 5, 2}, {1, 3, 6, 5, 2, 4}, {1, 3, 6, 5, 4, 2}, {1, 4, 2, 3, 5, 6}, {1, 4, 2, 3, 6, 5}, {1, 4, 2, 5, 3, 6}, {1, 4, 2, 5, 6, 3}, {1, 4, 2, 6, 3, 5}, {1, 4, 2, 6, 5, 3}, {1, 4, 3, 2, 5, 6}, {1, 4, 3, 2, 6, 5}, {1, 4, 3, 5, 2, 6}, {1, 4, 3, 5, 6, 2}, {1, 4, 3, 6, 2, 5}, {1, 4, 3, 6, 5, 2}, {1, 4, 5, 2, 3, 6}, {1, 4, 5, 2, 6, 3}, {1, 4, 5, 3, 2, 6}, {1, 4, 5, 3, 6, 2}, {1, 4, 5, 6, 2, 3}, {1, 4, 5, 6, 3, 2}, {1, 4, 6, 2, 3, 5}, {1, 4, 6, 2, 5, 3}, {1, 4, 6, 3, 2, 5}, {1, 4, 6, 3, 5, 2}, {1, 4, 6, 5, 2, 3}, {1, 4, 6, 5, 3, 2}, {1, 5, 2, 3, 4, 6}, {1, 5, 2, 3, 6, 4}, {1, 5, 2, 4, 3, 6}, {1, 5, 2, 4, 6, 3}, {1, 5, 2, 6, 3, 4}, {1, 5, 2, 6, 4, 3}, {1, 5, 3, 2, 4, 6}, {1, 5, 3, 2, 6, 4}, {1, 5, 3, 4, 2, 6}, {1, 5, 3, 4, 6, 2}, {1, 5, 3, 6, 2, 4}, {1, 5, 3, 6, 4, 2}, {1, 5, 4, 2, 3, 6}, {1, 5, 4, 2, 6, 3}, {1, 5, 4, 3, 2, 6}, {1, 5, 4, 3, 6, 2}, {1, 5, 4, 6, 2, 3}, {1, 5, 4, 6, 3, 2}, {1, 5, 6, 2, 3, 4}, {1, 5, 6, 2, 4, 3}, {1, 5, 6, 3, 2, 4}, {1, 5, 6, 3, 4, 2}, {1, 5, 6, 4, 2, 3}, {1, 5, 6, 4, 3, 2}, {1, 6, 2, 3, 4, 5}, {1, 6, 2, 3, 5, 4}, {1, 6, 2, 4, 3, 5}, {1, 6, 2, 4, 5, 3}, {1, 6, 2, 5, 3, 4}, {1, 6, 2, 5, 4, 3}, {1, 6, 3, 2, 4, 5}, {1, 6, 3, 2, 5, 4}, {1, 6, 3, 4, 2, 5}, {1, 6, 3, 4, 5, 2}, {1, 6, 3, 5, 2, 4}, {1, 6, 3, 5, 4, 2}, {1, 6, 4, 2, 3, 5}, {1, 6, 4, 2, 5, 3}, {1, 6, 4, 3, 2, 5}, {1, 6, 4, 3, 5, 2}, {1, 6, 4, 5, 2, 3}, {1, 6, 4, 5, 3, 2}, {1, 6, 5, 2, 3, 4}, {1, 6, 5, 2, 4, 3}, {1, 6, 5, 3, 2, 4}, {1, 6, 5, 3, 4, 2}, {1, 6, 5, 4, 2, 3}, {1, 6, 5, 4, 3, 2}, {2, 1, 3, 4, 5, 6}, {2, 1, 3, 4, 6, 5}, {2, 1, 3, 5, 4, 6}, {2, 1, 3, 5, 6, 4}, {2, 1, 3, 6, 4, 5}, {2, 1, 3, 6, 5, 4}, {2, 1, 4, 3, 5, 6}, {2, 1, 4, 3, 6, 5}, {2, 1, 4, 5, 3, 6}, {2, 1, 4, 5, 6, 3}, {2, 1, 4, 6, 3, 5}, {2, 1, 4, 6, 5, 3}, {2, 1, 5, 3, 4, 6}, {2, 1, 5, 3, 6, 4}, {2, 1, 5, 4, 3, 6}, {2, 1, 5, 4, 6, 3}, {2, 1, 5, 6, 3, 4}, {2, 1, 5, 6, 4, 3}, {2, 1, 6, 3, 4, 5}, {2, 1, 6, 3, 5, 4}, {2, 1, 6, 4, 3, 5}, {2, 1, 6, 4, 5, 3}, {2, 1, 6, 5, 3, 4}, {2, 1, 6, 5, 4, 3}, {2, 3, 1, 4, 5, 6}, {2, 3, 1, 4, 6, 5}, {2, 3, 1, 5, 4, 6}, {2, 3, 1, 5, 6, 4}, {2, 3, 1, 6, 4, 5}, {2, 3, 1, 6, 5, 4}, {2, 3, 4, 1, 5, 6}, {2, 3, 4, 1, 6, 5}, {2, 3, 4, 5, 1, 6}, {2, 3, 4, 5, 6, 1}, {2, 3, 4, 6, 1, 5}, {2, 3, 4, 6, 5, 1}, {2, 3, 5, 1, 4, 6}, {2, 3, 5, 1, 6, 4}, {2, 3, 5, 4, 1, 6}, {2, 3, 5, 4, 6, 1}, {2, 3, 5, 6, 1, 4}, {2, 3, 5, 6, 4, 1}, {2, 3, 6, 1, 4, 5}, {2, 3, 6, 1, 5, 4}, {2, 3, 6, 4, 1, 5}, {2, 3, 6, 4, 5, 1}, {2, 3, 6, 5, 1, 4}, {2, 3, 6, 5, 4, 1}, {2, 4, 1, 3, 5, 6}, {2, 4, 1, 3, 6, 5}, {2, 4, 1, 5, 3, 6}, {2, 4, 1, 5, 6, 3}, {2, 4, 1, 6, 3, 5}, {2, 4, 1, 6, 5, 3}, {2, 4, 3, 1, 5, 6}, {2, 4, 3, 1, 6, 5}, {2, 4, 3, 5, 1, 6}, {2, 4, 3, 5, 6, 1}, {2, 4, 3, 6, 1, 5}, {2, 4, 3, 6, 5, 1}, {2, 4, 5, 1, 3, 6}, {2, 4, 5, 1, 6, 3}, {2, 4, 5, 3, 1, 6}, {2, 4, 5, 3, 6, 1}, {2, 4, 5, 6, 1, 3}, {2, 4, 5, 6, 3, 1}, {2, 4, 6, 1, 3, 5}, {2, 4, 6, 1, 5, 3}, {2, 4, 6, 3, 1, 5}, {2, 4, 6, 3, 5, 1}, {2, 4, 6, 5, 1, 3}, {2, 4, 6, 5, 3, 1}, {2, 5, 1, 3, 4, 6}, {2, 5, 1, 3, 6, 4}, {2, 5, 1, 4, 3, 6}, {2, 5, 1, 4, 6, 3}, {2, 5, 1, 6, 3, 4}, {2, 5, 1, 6, 4, 3}, {2, 5, 3, 1, 4, 6}, {2, 5, 3, 1, 6, 4}, {2, 5, 3, 4, 1, 6}, {2, 5, 3, 4, 6, 1}, {2, 5, 3, 6, 1, 4}, {2, 5, 3, 6, 4, 1}, {2, 5, 4, 1, 3, 6}, {2, 5, 4, 1, 6, 3}, {2, 5, 4, 3, 1, 6}, {2, 5, 4, 3, 6, 1}, {2, 5, 4, 6, 1, 3}, {2, 5, 4, 6, 3, 1}, {2, 5, 6, 1, 3, 4}, {2, 5, 6, 1, 4, 3}, {2, 5, 6, 3, 1, 4}, {2, 5, 6, 3, 4, 1}, {2, 5, 6, 4, 1, 3}, {2, 5, 6, 4, 3, 1}, {2, 6, 1, 3, 4, 5}, {2, 6, 1, 3, 5, 4}, {2, 6, 1, 4, 3, 5}, {2, 6, 1, 4, 5, 3}, {2, 6, 1, 5, 3, 4}, {2, 6, 1, 5, 4, 3}, {2, 6, 3, 1, 4, 5}, {2, 6, 3, 1, 5, 4}, {2, 6, 3, 4, 1, 5}, {2, 6, 3, 4, 5, 1}, {2, 6, 3, 5, 1, 4}, {2, 6, 3, 5, 4, 1}, {2, 6, 4, 1, 3, 5}, {2, 6, 4, 1, 5, 3}, {2, 6, 4, 3, 1, 5}, {2, 6, 4, 3, 5, 1}, {2, 6, 4, 5, 1, 3}, {2, 6, 4, 5, 3, 1}, {2, 6, 5, 1, 3, 4}, {2, 6, 5, 1, 4, 3}, {2, 6, 5, 3, 1, 4}, {2, 6, 5, 3, 4, 1}, {2, 6, 5, 4, 1, 3}, {2, 6, 5, 4, 3, 1}, {3, 1, 2, 4, 5, 6}, {3, 1, 2, 4, 6, 5}, {3, 1, 2, 5, 4, 6}, {3, 1, 2, 5, 6, 4}, {3, 1, 2, 6, 4, 5}, {3, 1, 2, 6, 5, 4}, {3, 1, 4, 2, 5, 6}, {3, 1, 4, 2, 6, 5}, {3, 1, 4, 5, 2, 6}, {3, 1, 4, 5, 6, 2}, {3, 1, 4, 6, 2, 5}, {3, 1, 4, 6, 5, 2}, {3, 1, 5, 2, 4, 6}, {3, 1, 5, 2, 6, 4}, {3, 1, 5, 4, 2, 6}, {3, 1, 5, 4, 6, 2}, {3, 1, 5, 6, 2, 4}, {3, 1, 5, 6, 4, 2}, {3, 1, 6, 2, 4, 5}, {3, 1, 6, 2, 5, 4}, {3, 1, 6, 4, 2, 5}, {3, 1, 6, 4, 5, 2}, {3, 1, 6, 5, 2, 4}, {3, 1, 6, 5, 4, 2}, {3, 2, 1, 4, 5, 6}, {3, 2, 1, 4, 6, 5}, {3, 2, 1, 5, 4, 6}, {3, 2, 1, 5, 6, 4}, {3, 2, 1, 6, 4, 5}, {3, 2, 1, 6, 5, 4}, {3, 2, 4, 1, 5, 6}, {3, 2, 4, 1, 6, 5}, {3, 2, 4, 5, 1, 6}, {3, 2, 4, 5, 6, 1}, {3, 2, 4, 6, 1, 5}, {3, 2, 4, 6, 5, 1}, {3, 2, 5, 1, 4, 6}, {3, 2, 5, 1, 6, 4}, {3, 2, 5, 4, 1, 6}, {3, 2, 5, 4, 6, 1}, {3, 2, 5, 6, 1, 4}, {3, 2, 5, 6, 4, 1}, {3, 2, 6, 1, 4, 5}, {3, 2, 6, 1, 5, 4}, {3, 2, 6, 4, 1, 5}, {3, 2, 6, 4, 5, 1}, {3, 2, 6, 5, 1, 4}, {3, 2, 6, 5, 4, 1}, {3, 4, 1, 2, 5, 6}, {3, 4, 1, 2, 6, 5}, {3, 4, 1, 5, 2, 6}, {3, 4, 1, 5, 6, 2}, {3, 4, 1, 6, 2, 5}, {3, 4, 1, 6, 5, 2}, {3, 4, 2, 1, 5, 6}, {3, 4, 2, 1, 6, 5}, {3, 4, 2, 5, 1, 6}, {3, 4, 2, 5, 6, 1}, {3, 4, 2, 6, 1, 5}, {3, 4, 2, 6, 5, 1}, {3, 4, 5, 1, 2, 6}, {3, 4, 5, 1, 6, 2}, {3, 4, 5, 2, 1, 6}, {3, 4, 5, 2, 6, 1}, {3, 4, 5, 6, 1, 2}, {3, 4, 5, 6, 2, 1}, {3, 4, 6, 1, 2, 5}, {3, 4, 6, 1, 5, 2}, {3, 4, 6, 2, 1, 5}, {3, 4, 6, 2, 5, 1}, {3, 4, 6, 5, 1, 2}, {3, 4, 6, 5, 2, 1}, {3, 5, 1, 2, 4, 6}, {3, 5, 1, 2, 6, 4}, {3, 5, 1, 4, 2, 6}, {3, 5, 1, 4, 6, 2}, {3, 5, 1, 6, 2, 4}, {3, 5, 1, 6, 4, 2}, {3, 5, 2, 1, 4, 6}, {3, 5, 2, 1, 6, 4}, {3, 5, 2, 4, 1, 6}, {3, 5, 2, 4, 6, 1}, {3, 5, 2, 6, 1, 4}, {3, 5, 2, 6, 4, 1}, {3, 5, 4, 1, 2, 6}, {3, 5, 4, 1, 6, 2}, {3, 5, 4, 2, 1, 6}, {3, 5, 4, 2, 6, 1}, {3, 5, 4, 6, 1, 2}, {3, 5, 4, 6, 2, 1}, {3, 5, 6, 1, 2, 4}, {3, 5, 6, 1, 4, 2}, {3, 5, 6, 2, 1, 4}, {3, 5, 6, 2, 4, 1}, {3, 5, 6, 4, 1, 2}, {3, 5, 6, 4, 2, 1}, {3, 6, 1, 2, 4, 5}, {3, 6, 1, 2, 5, 4}, {3, 6, 1, 4, 2, 5}, {3, 6, 1, 4, 5, 2}, {3, 6, 1, 5, 2, 4}, {3, 6, 1, 5, 4, 2}, {3, 6, 2, 1, 4, 5}, {3, 6, 2, 1, 5, 4}, {3, 6, 2, 4, 1, 5}, {3, 6, 2, 4, 5, 1}, {3, 6, 2, 5, 1, 4}, {3, 6, 2, 5, 4, 1}, {3, 6, 4, 1, 2, 5}, {3, 6, 4, 1, 5, 2}, {3, 6, 4, 2, 1, 5}, {3, 6, 4, 2, 5, 1}, {3, 6, 4, 5, 1, 2}, {3, 6, 4, 5, 2, 1}, {3, 6, 5, 1, 2, 4}, {3, 6, 5, 1, 4, 2}, {3, 6, 5, 2, 1, 4}, {3, 6, 5, 2, 4, 1}, {3, 6, 5, 4, 1, 2}, {3, 6, 5, 4, 2, 1}, {4, 1, 2, 3, 5, 6}, {4, 1, 2, 3, 6, 5}, {4, 1, 2, 5, 3, 6}, {4, 1, 2, 5, 6, 3}, {4, 1, 2, 6, 3, 5}, {4, 1, 2, 6, 5, 3}, {4, 1, 3, 2, 5, 6}, {4, 1, 3, 2, 6, 5}, {4, 1, 3, 5, 2, 6}, {4, 1, 3, 5, 6, 2}, {4, 1, 3, 6, 2, 5}, {4, 1, 3, 6, 5, 2}, {4, 1, 5, 2, 3, 6}, {4, 1, 5, 2, 6, 3}, {4, 1, 5, 3, 2, 6}, {4, 1, 5, 3, 6, 2}, {4, 1, 5, 6, 2, 3}, {4, 1, 5, 6, 3, 2}, {4, 1, 6, 2, 3, 5}, {4, 1, 6, 2, 5, 3}, {4, 1, 6, 3, 2, 5}, {4, 1, 6, 3, 5, 2}, {4, 1, 6, 5, 2, 3}, {4, 1, 6, 5, 3, 2}, {4, 2, 1, 3, 5, 6}, {4, 2, 1, 3, 6, 5}, {4, 2, 1, 5, 3, 6}, {4, 2, 1, 5, 6, 3}, {4, 2, 1, 6, 3, 5}, {4, 2, 1, 6, 5, 3}, {4, 2, 3, 1, 5, 6}, {4, 2, 3, 1, 6, 5}, {4, 2, 3, 5, 1, 6}, {4, 2, 3, 5, 6, 1}, {4, 2, 3, 6, 1, 5}, {4, 2, 3, 6, 5, 1}, {4, 2, 5, 1, 3, 6}, {4, 2, 5, 1, 6, 3}, {4, 2, 5, 3, 1, 6}, {4, 2, 5, 3, 6, 1}, {4, 2, 5, 6, 1, 3}, {4, 2, 5, 6, 3, 1}, {4, 2, 6, 1, 3, 5}, {4, 2, 6, 1, 5, 3}, {4, 2, 6, 3, 1, 5}, {4, 2, 6, 3, 5, 1}, {4, 2, 6, 5, 1, 3}, {4, 2, 6, 5, 3, 1}, {4, 3, 1, 2, 5, 6}, {4, 3, 1, 2, 6, 5}, {4, 3, 1, 5, 2, 6}, {4, 3, 1, 5, 6, 2}, {4, 3, 1, 6, 2, 5}, {4, 3, 1, 6, 5, 2}, {4, 3, 2, 1, 5, 6}, {4, 3, 2, 1, 6, 5}, {4, 3, 2, 5, 1, 6}, {4, 3, 2, 5, 6, 1}, {4, 3, 2, 6, 1, 5}, {4, 3, 2, 6, 5, 1}, {4, 3, 5, 1, 2, 6}, {4, 3, 5, 1, 6, 2}, {4, 3, 5, 2, 1, 6}, {4, 3, 5, 2, 6, 1}, {4, 3, 5, 6, 1, 2}, {4, 3, 5, 6, 2, 1}, {4, 3, 6, 1, 2, 5}, {4, 3, 6, 1, 5, 2}, {4, 3, 6, 2, 1, 5}, {4, 3, 6, 2, 5, 1}, {4, 3, 6, 5, 1, 2}, {4, 3, 6, 5, 2, 1}, {4, 5, 1, 2, 3, 6}, {4, 5, 1, 2, 6, 3}, {4, 5, 1, 3, 2, 6}, {4, 5, 1, 3, 6, 2}, {4, 5, 1, 6, 2, 3}, {4, 5, 1, 6, 3, 2}, {4, 5, 2, 1, 3, 6}, {4, 5, 2, 1, 6, 3}, {4, 5, 2, 3, 1, 6}, {4, 5, 2, 3, 6, 1}, {4, 5, 2, 6, 1, 3}, {4, 5, 2, 6, 3, 1}, {4, 5, 3, 1, 2, 6}, {4, 5, 3, 1, 6, 2}, {4, 5, 3, 2, 1, 6}, {4, 5, 3, 2, 6, 1}, {4, 5, 3, 6, 1, 2}, {4, 5, 3, 6, 2, 1}, {4, 5, 6, 1, 2, 3}, {4, 5, 6, 1, 3, 2}, {4, 5, 6, 2, 1, 3}, {4, 5, 6, 2, 3, 1}, {4, 5, 6, 3, 1, 2}, {4, 5, 6, 3, 2, 1}, {4, 6, 1, 2, 3, 5}, {4, 6, 1, 2, 5, 3}, {4, 6, 1, 3, 2, 5}, {4, 6, 1, 3, 5, 2}, {4, 6, 1, 5, 2, 3}, {4, 6, 1, 5, 3, 2}, {4, 6, 2, 1, 3, 5}, {4, 6, 2, 1, 5, 3}, {4, 6, 2, 3, 1, 5}, {4, 6, 2, 3, 5, 1}, {4, 6, 2, 5, 1, 3}, {4, 6, 2, 5, 3, 1}, {4, 6, 3, 1, 2, 5}, {4, 6, 3, 1, 5, 2}, {4, 6, 3, 2, 1, 5}, {4, 6, 3, 2, 5, 1}, {4, 6, 3, 5, 1, 2}, {4, 6, 3, 5, 2, 1}, {4, 6, 5, 1, 2, 3}, {4, 6, 5, 1, 3, 2}, {4, 6, 5, 2, 1, 3}, {4, 6, 5, 2, 3, 1}, {4, 6, 5, 3, 1, 2}, {4, 6, 5, 3, 2, 1}, {5, 1, 2, 3, 4, 6}, {5, 1, 2, 3, 6, 4}, {5, 1, 2, 4, 3, 6}, {5, 1, 2, 4, 6, 3}, {5, 1, 2, 6, 3, 4}, {5, 1, 2, 6, 4, 3}, {5, 1, 3, 2, 4, 6}, {5, 1, 3, 2, 6, 4}, {5, 1, 3, 4, 2, 6}, {5, 1, 3, 4, 6, 2}, {5, 1, 3, 6, 2, 4}, {5, 1, 3, 6, 4, 2}, {5, 1, 4, 2, 3, 6}, {5, 1, 4, 2, 6, 3}, {5, 1, 4, 3, 2, 6}, {5, 1, 4, 3, 6, 2}, {5, 1, 4, 6, 2, 3}, {5, 1, 4, 6, 3, 2}, {5, 1, 6, 2, 3, 4}, {5, 1, 6, 2, 4, 3}, {5, 1, 6, 3, 2, 4}, {5, 1, 6, 3, 4, 2}, {5, 1, 6, 4, 2, 3}, {5, 1, 6, 4, 3, 2}, {5, 2, 1, 3, 4, 6}, {5, 2, 1, 3, 6, 4}, {5, 2, 1, 4, 3, 6}, {5, 2, 1, 4, 6, 3}, {5, 2, 1, 6, 3, 4}, {5, 2, 1, 6, 4, 3}, {5, 2, 3, 1, 4, 6}, {5, 2, 3, 1, 6, 4}, {5, 2, 3, 4, 1, 6}, {5, 2, 3, 4, 6, 1}, {5, 2, 3, 6, 1, 4}, {5, 2, 3, 6, 4, 1}, {5, 2, 4, 1, 3, 6}, {5, 2, 4, 1, 6, 3}, {5, 2, 4, 3, 1, 6}, {5, 2, 4, 3, 6, 1}, {5, 2, 4, 6, 1, 3}, {5, 2, 4, 6, 3, 1}, {5, 2, 6, 1, 3, 4}, {5, 2, 6, 1, 4, 3}, {5, 2, 6, 3, 1, 4}, {5, 2, 6, 3, 4, 1}, {5, 2, 6, 4, 1, 3}, {5, 2, 6, 4, 3, 1}, {5, 3, 1, 2, 4, 6}, {5, 3, 1, 2, 6, 4}, {5, 3, 1, 4, 2, 6}, {5, 3, 1, 4, 6, 2}, {5, 3, 1, 6, 2, 4}, {5, 3, 1, 6, 4, 2}, {5, 3, 2, 1, 4, 6}, {5, 3, 2, 1, 6, 4}, {5, 3, 2, 4, 1, 6}, {5, 3, 2, 4, 6, 1}, {5, 3, 2, 6, 1, 4}, {5, 3, 2, 6, 4, 1}, {5, 3, 4, 1, 2, 6}, {5, 3, 4, 1, 6, 2}, {5, 3, 4, 2, 1, 6}, {5, 3, 4, 2, 6, 1}, {5, 3, 4, 6, 1, 2}, {5, 3, 4, 6, 2, 1}, {5, 3, 6, 1, 2, 4}, {5, 3, 6, 1, 4, 2}, {5, 3, 6, 2, 1, 4}, {5, 3, 6, 2, 4, 1}, {5, 3, 6, 4, 1, 2}, {5, 3, 6, 4, 2, 1}, {5, 4, 1, 2, 3, 6}, {5, 4, 1, 2, 6, 3}, {5, 4, 1, 3, 2, 6}, {5, 4, 1, 3, 6, 2}, {5, 4, 1, 6, 2, 3}, {5, 4, 1, 6, 3, 2}, {5, 4, 2, 1, 3, 6}, {5, 4, 2, 1, 6, 3}, {5, 4, 2, 3, 1, 6}, {5, 4, 2, 3, 6, 1}, {5, 4, 2, 6, 1, 3}, {5, 4, 2, 6, 3, 1}, {5, 4, 3, 1, 2, 6}, {5, 4, 3, 1, 6, 2}, {5, 4, 3, 2, 1, 6}, {5, 4, 3, 2, 6, 1}, {5, 4, 3, 6, 1, 2}, {5, 4, 3, 6, 2, 1}, {5, 4, 6, 1, 2, 3}, {5, 4, 6, 1, 3, 2}, {5, 4, 6, 2, 1, 3}, {5, 4, 6, 2, 3, 1}, {5, 4, 6, 3, 1, 2}, {5, 4, 6, 3, 2, 1}, {5, 6, 1, 2, 3, 4}, {5, 6, 1, 2, 4, 3}, {5, 6, 1, 3, 2, 4}, {5, 6, 1, 3, 4, 2}, {5, 6, 1, 4, 2, 3}, {5, 6, 1, 4, 3, 2}, {5, 6, 2, 1, 3, 4}, {5, 6, 2, 1, 4, 3}, {5, 6, 2, 3, 1, 4}, {5, 6, 2, 3, 4, 1}, {5, 6, 2, 4, 1, 3}, {5, 6, 2, 4, 3, 1}, {5, 6, 3, 1, 2, 4}, {5, 6, 3, 1, 4, 2}, {5, 6, 3, 2, 1, 4}, {5, 6, 3, 2, 4, 1}, {5, 6, 3, 4, 1, 2}, {5, 6, 3, 4, 2, 1}, {5, 6, 4, 1, 2, 3}, {5, 6, 4, 1, 3, 2}, {5, 6, 4, 2, 1, 3}, {5, 6, 4, 2, 3, 1}, {5, 6, 4, 3, 1, 2}, {5, 6, 4, 3, 2, 1}, {6, 1, 2, 3, 4, 5}, {6, 1, 2, 3, 5, 4}, {6, 1, 2, 4, 3, 5}, {6, 1, 2, 4, 5, 3}, {6, 1, 2, 5, 3, 4}, {6, 1, 2, 5, 4, 3}, {6, 1, 3, 2, 4, 5}, {6, 1, 3, 2, 5, 4}, {6, 1, 3, 4, 2, 5}, {6, 1, 3, 4, 5, 2}, {6, 1, 3, 5, 2, 4}, {6, 1, 3, 5, 4, 2}, {6, 1, 4, 2, 3, 5}, {6, 1, 4, 2, 5, 3}, {6, 1, 4, 3, 2, 5}, {6, 1, 4, 3, 5, 2}, {6, 1, 4, 5, 2, 3}, {6, 1, 4, 5, 3, 2}, {6, 1, 5, 2, 3, 4}, {6, 1, 5, 2, 4, 3}, {6, 1, 5, 3, 2, 4}, {6, 1, 5, 3, 4, 2}, {6, 1, 5, 4, 2, 3}, {6, 1, 5, 4, 3, 2}, {6, 2, 1, 3, 4, 5}, {6, 2, 1, 3, 5, 4}, {6, 2, 1, 4, 3, 5}, {6, 2, 1, 4, 5, 3}, {6, 2, 1, 5, 3, 4}, {6, 2, 1, 5, 4, 3}, {6, 2, 3, 1, 4, 5}, {6, 2, 3, 1, 5, 4}, {6, 2, 3, 4, 1, 5}, {6, 2, 3, 4, 5, 1}, {6, 2, 3, 5, 1, 4}, {6, 2, 3, 5, 4, 1}, {6, 2, 4, 1, 3, 5}, {6, 2, 4, 1, 5, 3}, {6, 2, 4, 3, 1, 5}, {6, 2, 4, 3, 5, 1}, {6, 2, 4, 5, 1, 3}, {6, 2, 4, 5, 3, 1}, {6, 2, 5, 1, 3, 4}, {6, 2, 5, 1, 4, 3}, {6, 2, 5, 3, 1, 4}, {6, 2, 5, 3, 4, 1}, {6, 2, 5, 4, 1, 3}, {6, 2, 5, 4, 3, 1}, {6, 3, 1, 2, 4, 5}, {6, 3, 1, 2, 5, 4}, {6, 3, 1, 4, 2, 5}, {6, 3, 1, 4, 5, 2}, {6, 3, 1, 5, 2, 4}, {6, 3, 1, 5, 4, 2}, {6, 3, 2, 1, 4, 5}, {6, 3, 2, 1, 5, 4}, {6, 3, 2, 4, 1, 5}, {6, 3, 2, 4, 5, 1}, {6, 3, 2, 5, 1, 4}, {6, 3, 2, 5, 4, 1}, {6, 3, 4, 1, 2, 5}, {6, 3, 4, 1, 5, 2}, {6, 3, 4, 2, 1, 5}, {6, 3, 4, 2, 5, 1}, {6, 3, 4, 5, 1, 2}, {6, 3, 4, 5, 2, 1}, {6, 3, 5, 1, 2, 4}, {6, 3, 5, 1, 4, 2}, {6, 3, 5, 2, 1, 4}, {6, 3, 5, 2, 4, 1}, {6, 3, 5, 4, 1, 2}, {6, 3, 5, 4, 2, 1}, {6, 4, 1, 2, 3, 5}, {6, 4, 1, 2, 5, 3}, {6, 4, 1, 3, 2, 5}, {6, 4, 1, 3, 5, 2}, {6, 4, 1, 5, 2, 3}, {6, 4, 1, 5, 3, 2}, {6, 4, 2, 1, 3, 5}, {6, 4, 2, 1, 5, 3}, {6, 4, 2, 3, 1, 5}, {6, 4, 2, 3, 5, 1}, {6, 4, 2, 5, 1, 3}, {6, 4, 2, 5, 3, 1}, {6, 4, 3, 1, 2, 5}, {6, 4, 3, 1, 5, 2}, {6, 4, 3, 2, 1, 5}, {6, 4, 3, 2, 5, 1}, {6, 4, 3, 5, 1, 2}, {6, 4, 3, 5, 2, 1}, {6, 4, 5, 1, 2, 3}, {6, 4, 5, 1, 3, 2}, {6, 4, 5, 2, 1, 3}, {6, 4, 5, 2, 3, 1}, {6, 4, 5, 3, 1, 2}, {6, 4, 5, 3, 2, 1}, {6, 5, 1, 2, 3, 4}, {6, 5, 1, 2, 4, 3}, {6, 5, 1, 3, 2, 4}, {6, 5, 1, 3, 4, 2}, {6, 5, 1, 4, 2, 3}, {6, 5, 1, 4, 3, 2}, {6, 5, 2, 1, 3, 4}, {6, 5, 2, 1, 4, 3}, {6, 5, 2, 3, 1, 4}, {6, 5, 2, 3, 4, 1}, {6, 5, 2, 4, 1, 3}, {6, 5, 2, 4, 3, 1}, {6, 5, 3, 1, 2, 4}, {6, 5, 3, 1, 4, 2}, {6, 5, 3, 2, 1, 4}, {6, 5, 3, 2, 4, 1}, {6, 5, 3, 4, 1, 2}, {6, 5, 3, 4, 2, 1}, {6, 5, 4, 1, 2, 3}, {6, 5, 4, 1, 3, 2}, {6, 5, 4, 2, 1, 3}, {6, 5, 4, 2, 3, 1}, {6, 5, 4, 3, 1, 2}, {6, 5, 4, 3, 2, 1}}

Note: This is a lazy person's solution !!! If I made a mistake, count them from the top !!!!!

Feb 3, 2018
#2
+101733
+1

Hi Guest, you have not done it the lazy way, you have done it the most straight forward (and long) way.

I'll see if I get the same answer...

All the 720 arrangements of the digits 1 through 6 are put in numerical order. What is the 428th term?

How many are between 100 000 and 199 000   That would be 1*5! = 120

200 000 - 299 000    That would also be 1*5! = 120

300 000 - 399 000    That would also be 1*5! = 120

So that is 360 so far    428-360= 68 more...

So it is going to be between 400,000 and 499,999

How many between 410,000 and 419,999

the position of the 4 and the 1 is set so that would be   4! = 24         68-24= 44 more to go

How many between 420,000 and 429,999. Another 24                     44-24=20 more to go

So it is going to be between 430,000 and 439,999

How many between 431,000 and 431,999.     3!=6

How many between 432,000 and 432,999.     3!=6

We canot repeat the 3 or the 4 at the front so

How many between 435,000 and 435,999.     3!=6                             20-18=2 more to go

Next is 436 125, then 436,215

So I think 436,215 is the 428th term.     That is what I get

check

120+120+120+24+24+6+6+6+2 = 428  Seems ok

they are not the same so one of us has made a mistake

Feb 4, 2018
#3
+1

Thanks Melody! The reason I said it was " a lazy person's solution" was because I simply wrote a few lines of computer code and it spat them out in seconds!! It also did the counting from the top!! It could very well have a small bug in it as far as counting is concerned. I might go through it and see if I can spot it!!.

Feb 4, 2018
#4
+101733
0

Thanks, there could be a 'bug' in my logic too ://

Melody  Feb 4, 2018